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%I #16 Sep 07 2018 04:42:26
%S 1,1,2,1,2,2,2,1,3,2,2,2,2,2,4,1,2,3,2,2,4,2,2,2,3,2,4,2,2,4,2,1,4,2,
%T 4,3,2,2,4,2,2,4,2,2,6,2,2,2,3,3,4,2,2,4,4,2,4,2,2,4,2,2,5,1,4,4,2,2,
%U 4,4,2,3,2,2,6,2,4,4,2,2,5,2,2,4,4,2,4,2,2,6,4,2,4,2,4,2,2,3,6,3,2,4,2,2,8
%N Number of distinct subset-products of the integer partition with Heinz number n.
%C A subset-product of an integer partition y is a product of some submultiset of y. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C Number of distinct values obtained when A003963 is applied to all divisors of n. - _Antti Karttunen_, Sep 05 2018
%H Antti Karttunen, <a href="/A301957/b301957.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%e The distinct subset-products of (4,2,1,1) are 1, 2, 4, and 8, so a(84) = 4.
%e The distinct subset-products of (6,3,2) are 1, 2, 3, 6, 12, 18, and 36, so a(195) = 7.
%t Table[If[n===1,1,Length[Union[Times@@@Subsets[Join@@Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]]],{n,100}]
%o (PARI)
%o up_to = 65537;
%o A003963(n) = { n=factor(n); n[, 1]=apply(primepi, n[, 1]); factorback(n) }; \\ From A003963
%o v003963 = vector(up_to,n,A003963(n));
%o A301957(n) = { my(m=Map(),s,k=0,c); fordiv(n,d,if(!mapisdefined(m,s = v003963[d],&c), mapput(m,s,s); k++)); (k); }; \\ _Antti Karttunen_, Sep 05 2018
%Y Cf. A000712, A001055, A001227, A002865, A003963, A108917, A162247, A276024, A292886, A301854, A301855, A301856, A301970, A301979, A304793.
%K nonn
%O 1,3
%A _Gus Wiseman_, Mar 29 2018
%E More terms from _Antti Karttunen_, Sep 05 2018
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