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A316555
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Number of distinct GCDs of nonempty submultisets of the integer partition with Heinz number n.
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5
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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
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OFFSET
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1,6
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Table[Length[Union[GCD@@@Rest[Subsets[If[n==1, {}, Cases[FactorInteger[n], {p_, k_}:>PrimePi[p]]]]]]], {n, 100}]
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PROG
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(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
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CROSSREFS
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Cf. A056239, A108917, A122768, A275972, A289508, A289509, A296150, A316313, A316314, A316430, A316556, A316557.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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