A020646 Least positive integer k for which 7^n divides k!.

1, 7, 14, 21, 28, 35, 42, 49, 49, 56, 63, 70, 77, 84, 91, 98, 98, 105, 112, 119, 126, 133, 140, 147, 147, 154, 161, 168, 175, 182, 189, 196, 196, 203, 210, 217, 224, 231, 238, 245, 245, 252, 259, 266, 273, 280, 287, 294, 294, 301, 308, 315, 322, 329, 336, 343, 343, 343, 350

Offset

0,2

References

H. Ibstedt, Smarandache Primitive Numbers, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 216-229.

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

F. Smarandache, Only Problems, Not Solutions!

Mathematica

lpi[n_]:=Module[{k = 1, n7 = 7^n}, While[! Divisible[k!, n7], k++]; k]; Array[lpi, 60, 0] (* Harvey P. Dale, Jun 29 2017 *)

Prog

(PARI) a(n) = {k = 1; while (valuation(k!, 7) < n, k++); k; } \\ Michel Marcus, Aug 19 2013
(Python)
from itertools import count
from sympy import multiplicity
def A020646(n):
    if n == 0: return 1
    c = 0
    for k in count(7, 7):
        c += multiplicity(7, k)
        if c+k+7 > n:
            return 7*(max(k, n-c) if n>=7 else n+1-c) # Chai Wah Wu, Feb 24 2026

Crossrefs

Cf. A007843, A007844, A007845.

Sequence in context: A289398 A044892 A004959 * A382413 A182341 A008589

Adjacent sequences: A020643 A020644 A020645 * A020647 A020648 A020649

Keyword

nonn

Author

David W. Wilson

Status

approved