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A129365 a(n)=A092287(n)/A129364(n). 4
1, 1, 1, 1, 1, 2, 2, 2, 6, 48, 48, 48, 48, 1536, 207360, 207360, 207360, 1105920, 1105920, 17694720, 30098718720, 15410543984640, 15410543984640, 481579499520, 60197437440000, 123284351877120000, 29958097506140160000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Conjectures: A) a(n) is always an integer. B) If p is a prime then p|a(n) if and only if p <= n/3. Let ordp(n,p) denote the exponent of the largest power of p which divides n. For example, ordp(48,2)=4 since 48=3*(2^4). The precise decomposition of a(n) into primes would follow from the following two conjectures: C) For each positive integer n and prime p, ordp(a(np),p)= ordp(a(np+1),p)= ordp(a(np+2),p)= . . . = ordp(a(np+p-1),p). D) Let b(n)=A004125(n). Then ordp(a(np),p)= b(n)+ b(floor(n/p))+ b(floor(n/p^2))+ b(floor(n/p^3))+ . . .. This is reminiscent of de Polignac's formula (also due to Legendre) for the prime factorization of n! (see the link).

LINKS

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

Wikipedia, De Polignac's formula.

FORMULA

a(n)=(product{j=1..n}product{k=1..n} gcd(j,k))/(product{j=1..n}product{d|j} d^(j/d)). a(n)=(product{j=1..n}product{k=1..n}gcd(j,k))/(product{k=1..n}(floor(n/k)!)^k).

CROSSREFS

Cf. A004125, A092287, A129364.

Sequence in context: A101416 A098920 A270557 * A125838 A021453 A053789

Adjacent sequences:  A129362 A129363 A129364 * A129366 A129367 A129368

KEYWORD

easy,nonn

AUTHOR

Peter Bala, Apr 13 2007

STATUS

approved

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)