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 A316555 Number of distinct GCDs of nonempty submultisets of the integer partition with Heinz number n. 5
 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 3, 2, 3, 2, 1, 2, 2, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 2, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 3, 1, 2, 1, 2, 1, 3, 3, 2, 2, 2, 1, 3, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 3, 1, 2, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). Number of distinct values obtained when A289508 is applied to all divisors of n larger than one. - Antti Karttunen, Sep 28 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 EXAMPLE 455 is the Heinz number of (6,4,3) which has possible GCDs of nonempty submultisets {1,2,3,4,6} so a(455) = 5. MATHEMATICA Table[Length[Union[GCD@@@Rest[Subsets[If[n==1, {}, Cases[FactorInteger[n], {p_, k_}:>PrimePi[p]]]]]]], {n, 100}] PROG (PARI) A289508(n) = gcd(apply(p->primepi(p), factor(n)[, 1])); A316555(n) = { my(m=Map(), s, k=0); fordiv(n, d, if((d>1)&&!mapisdefined(m, s=A289508(d)), mapput(m, s, s); k++)); (k); }; \\ Antti Karttunen, Sep 28 2018 CROSSREFS Cf. A056239, A108917, A122768, A275972, A289508, A289509, A296150, A316313, A316314, A316430, A316556, A316557. Cf. also A304793, A305611, A319685, A319695 for other similarly constructed sequences. Sequence in context: A008647 A036475 A330746 * A337531 A316556 A187279 Adjacent sequences: A316552 A316553 A316554 * A316556 A316557 A316558 KEYWORD nonn AUTHOR Gus Wiseman, Jul 06 2018 EXTENSIONS More terms from Antti Karttunen, Sep 28 2018 STATUS approved

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Last modified February 2 16:53 EST 2023. Contains 360023 sequences. (Running on oeis4.)