TopCoder Statistics - Problem Statement

Problem Statement

The function g(n, p) is defined for all positive integers n and all primes p. Its definition is as follows:

if n is not divisible by p:
    g(n,p) = 0
otherwise:
    g(n,p) = the largest power of p that does not exceed n

The function f(n) is defined for all positive integers as follows: f(n) is the sum of g(n,p) over all primes p.

You are given an int X. Compute and return the exact value of the sum f(1) + f(2) + ... + f(X).

Definition

Class:: SimpleMathProblemDiv1
Method:: calculate
Parameters:: long
Returns:: long
Method signature:: long calculate(long X)
(be sure your method is public)

Notes

You may assume that the largest possible output fits into a long.

Constraints

X will be between 1 and 3,333,377,777, inclusive.

Examples

1

Returns: 0
8

Returns: 36
15

Returns: 128
777444111

Returns: 342683738130575177
2

Returns: 2
3

Returns: 5
4

Returns: 9
5

Returns: 14
6

Returns: 21
7

Returns: 28
9

Returns: 45
30

Returns: 518
35

Returns: 700
89

Returns: 4453
88

Returns: 4364
40

Returns: 944
951

Returns: 518261
549

Returns: 168554
669

Returns: 252713
535

Returns: 159878
617

Returns: 213423
4558

Returns: 12206178
9886

Returns: 56237130
6332

Returns: 22823991
2395

Returns: 3143609
78298

Returns: 3373110161
41373

Returns: 1012381338
73147

Returns: 2927153443
74818

Returns: 3070489928
35008

Returns: 726305765
517662

Returns: 147018695705
517080

Returns: 146721897863
852803

Returns: 416149194998
297023

Returns: 51096940813
3950328

Returns: 8746728745655
9775158

Returns: 54625604183596
3319658

Returns: 6452551133605
4485004

Returns: 11074329492874
67223642

Returns: 2643075611119206
67905677

Returns: 2706868743156309
61838822

Returns: 2235400870651969
30945529

Returns: 527510126975375
59167178

Returns: 2047635007854376
743871768

Returns: 316739447375556073
400702621

Returns: 91875180835272892
253542755

Returns: 34741944770427850
204789971

Returns: 23439598799767782
616617635

Returns: 221683308757025191
1898461266

Returns: 2061586642882203503
1627383434

Returns: 1549198167936240885
1702543013

Returns: 1689334861001660324
1661677491

Returns: 1613016782507267974
1940693304

Returns: 2143262971707200654
1987316407

Returns: 2236216164699706625
1267449406

Returns: 897905692186351026
1451670421

Returns: 1226465623568923595
1601681771

Returns: 1501480207208827573
1514002006

Returns: 1339950981029778622
2131442973

Returns: 2555900362266747569
2998099957

Returns: 5189362099103820101
2551480298

Returns: 3770912908255148536
2802768357

Returns: 4562810769962276053
2957475841

Returns: 5058082341249917206
2004552794

Returns: 2274088811224605557
2607248258

Returns: 3944571494214423011
2540726564

Returns: 3738033662370291947
2076906246

Returns: 2433619288649866963
2975043127

Returns: 5114809539839103289
3333377777

Returns: 6294700701212792329
3208733377

Returns: 5879755621198364667
3138024373

Returns: 5646149889202573866
3214603023

Returns: 5899182293665341972
3198327292

Returns: 5845321883235522358
3131222766

Returns: 5623716753944497650
3064069447

Returns: 5403127583601271120
3001041161

Returns: 5198877152586814676
3087666137

Returns: 5480230152539719133
3007258080

Returns: 5218993086628418571
3252828481

Returns: 6025813772453043356

Statistics

Problem Statement for "SimpleMathProblemDiv1"

Problem Statement

Definition

Notes

Constraints

Examples