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A163176 The n-th Minkowski number divided by the n-th factorial: a(n) = A053657(n)/n!. 5
1, 1, 4, 2, 48, 16, 576, 144, 3840, 768, 9216, 1536, 3870720, 552960, 442368, 55296, 26542080, 2949120, 2229534720, 222953472, 70071091200, 6370099200, 76441190400, 6370099200, 16694755983360, 1284211998720, 570760888320 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) is an integer by Legendre's formula for the exponent of the highest power of a prime dividing n!.

a(2n-1) = n*a(2n) because A053657(2n) = 2*A053657(2n-1).

See A053657 for additional comments, references, and links.

REFERENCES

J.-L. Chabert, Integer-valued polynomials on prime numbers and logarithm power expansion, European J. Combinatorics 28 (2007) 754-761.

LINKS

Table of n, a(n) for n=1..27.

F. Bencherif, Sur une propriete des polynomes de Stirling

FORMULA

a(n) = (1/n!)*Prod_{p prime} p^{Sum_{k>=0} [(n-1)/((p-1)p^k)]}.

EXAMPLE

a(4) = A053657(4)/4! = 48/24 = 2.

MAPLE

Contribution from Peter Luschny, Jul 26 2009: (Start)

A163176 := proc(n) local L, p;

L := proc(n, p, r) local q, s; q := p-r; s := 0;

do if q > n then break fi; s := s+iquo(n, q);

q := q*p od; s end; mul(p^(L(n-1, p, 1)-L(n, p, 0)),

p = select(isprime, [$2..n])) end: (End)

MATHEMATICA

a[n_] := (1/n!)*Product[ p^Sum[ Floor[ (n-1)/((p-1)*p^k) ], {k, 0, n}], {p, Select[ Range[2, n], PrimeQ]}]; Table[ a[n], {n, 1, 27}] (* Jean-Fran├žois Alcover, Dec 07 2011 *)

CROSSREFS

Cf. A053657.

Sequence in context: A120968 A193894 A107667 * A277306 A201444 A236381

Adjacent sequences:  A163173 A163174 A163175 * A163177 A163178 A163179

KEYWORD

easy,nonn

AUTHOR

Jonathan Sondow, Jul 24 2009

STATUS

approved

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Last modified February 19 18:31 EST 2018. Contains 299356 sequences. (Running on oeis4.)