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A327512
Maximum divisor of n that is 1, 2, or a nonprime number whose prime indices are pairwise coprime.
3
1, 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, 12, 1, 14, 15, 16, 1, 6, 1, 20, 1, 22, 1, 24, 1, 26, 1, 28, 1, 30, 1, 32, 33, 34, 35, 12, 1, 38, 1, 40, 1, 14, 1, 44, 15, 46, 1, 48, 1, 10, 51, 52, 1, 6, 55, 56, 1, 58, 1, 60, 1, 62, 1, 64, 1, 66, 1, 68, 69, 70, 1, 24, 1, 74
OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Numbers that are 1, 2, or a nonprime number whose prime indices are pairwise coprime are listed in A302696, which is the union of this sequence.
a(n) is the greatest term of A302696 which divides n. - Antti Karttunen, Dec 06 2021
EXAMPLE
The divisors of 72 that are 1, 2, or nonprime numbers whose prime indices are pairwise coprime are: {1, 2, 4, 6, 8, 12, 24}, so a(72) = 24.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Max[Select[Divisors[n], #==1||CoprimeQ@@primeMS[#]&]], {n, 100}]
PROG
(PARI)
isA302696(n) = if(isprimepower(n), !(n%2), if(!issquarefree(n>>valuation(n, 2)), 0, my(pis=apply(primepi, factor(n)[, 1])); (lcm(pis)==factorback(pis))));
A327512(n) = vecmax(select(isA302696, divisors(n))); \\ Antti Karttunen, Dec 06 2021
CROSSREFS
See link for additional cross-references.
Sequence in context: A214060 A009531 A124625 * A327529 A318775 A317500
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 19 2019
STATUS
approved