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A090623 Triangle of T(n,k) = [n/k] + [n/k^2] + [n/k^3] + [n/k^4] + ... for n, k > 1. 3
1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 4, 2, 1, 1, 1, 4, 2, 1, 1, 1, 1, 7, 2, 2, 1, 1, 1, 1, 7, 4, 2, 1, 1, 1, 1, 1, 8, 4, 2, 1, 1, 1, 1, 1, 1, 8, 4, 2, 1, 1, 1, 1, 1, 1, 1, 10, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 10, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,4

LINKS

Table of n, a(n) for n=2..104.

Wenguang Zhai, On the prime power factorization of n!, Journal of Number Theory, Volume 129, Issue 8, August 2009, Pages 1820-1836.

FORMULA

For p prime, T(n, p) = A090622(n, p) is the number of times that p is a factor of n!.

EXAMPLE

Rows start:

1;

1,1;

3,1,1;

3,1,1,1;

4,2,1,1,1;

4,2,1,1,1,1;

7,2,2,1,1,1,1;

7,4,2,1,1,1,1,1;

8,4,2,1,1,1,1,1,1;

etc.

PROG

(PARI) t(n, k) = {my(s = 0, j = 1); while(p=n\k^j, s += p; j++); s; } \\ Michel Marcus, Feb 02 2016

CROSSREFS

Rows include A011371, A054861, A054893, A027868, A054895, A054896, A054897, A054898, A054899, A064458, A064459, A090620, A054900.

Sequence in context: A110268 A058965 A226306 * A098094 A087283 A111625

Adjacent sequences:  A090620 A090621 A090622 * A090624 A090625 A090626

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Dec 06 2003

STATUS

approved

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Last modified July 21 21:14 EDT 2019. Contains 325199 sequences. (Running on oeis4.)