LINKS
Robert Israel, <a href="/A325703/b325703_1.txt">Table of n, a(n) for n = 1..3168</a>
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Revision History for A325703
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
If n = prime(i_1)^j_1 * ... * prime(i_k)^j_k, then a(n) is the denominator of the reciprocal factorial sum j_1/i_1! + ... + j_k/i_k!.
(history; published version)
(history; published version)
STATUS
proposed
approved
STATUS
editing
proposed
KEYWORD
nonn,frac,changed,look
LINKS
Robert Israel, <a href="/A325703/b325703_1.txt">Table of n, a(n) for n = 1..3168</a>
MAPLE
f:= proc(n) local F, t;
F:= ifactors(n)[2];
denom(add(t[2]/numtheory:-pi(t[1])!, t=F))
end proc:
map(f, [$1..100]); # Robert Israel, Oct 13 2024
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
NAME
allocated for Gus WisemanIf n = prime(i_1)^j_1 * ... * prime(i_k)^j_k, then a(n) is the denominator of the reciprocal factorial sum j_1/i_1! + ... + j_k/i_k!.
DATA
1, 1, 2, 1, 6, 2, 24, 1, 1, 6, 120, 2, 720, 24, 3, 1, 5040, 1, 40320, 6, 24, 120, 362880, 2, 3, 720, 2, 24, 3628800, 3, 39916800, 1, 120, 5040, 24, 1, 479001600, 40320, 720, 6, 6227020800, 24, 87178291200, 120, 6, 362880, 1307674368000, 2, 12, 3, 5040, 720
OFFSET
1,3
COMMENTS
Alternatively, if n = prime(i_1) * ... * prime(i_k), then a(n) is the denominator of 1/i_1! + ... + 1/i_k!.
LINKS
Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
MATHEMATICA
Table[Total[Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>k/PrimePi[p]!]], {n, 100}]//Denominator
CROSSREFS
KEYWORD
allocated
nonn,frac
AUTHOR
Gus Wiseman, May 18 2019
STATUS
approved
editing