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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A304795 Number of positive special sums of the integer partition with Heinz number n.

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%I A304795 #13 Jul 03 2018 03:24:31
%S A304795 0,1,1,2,1,3,1,3,2,3,1,3,1,3,3,4,1,5,1,5,3,3,1,3,2,3,3,5,1,5,1,5,3,3,
%T A304795 3,4,1,3,3,5,1,7,1,5,5,3,1,3,2,5,3,5,1,7,3,7,3,3,1,3,1,3,3,6,3,7,1,5,
%U A304795 3,5,1,3,1,3,5,5,3,7,1,5,4,3,1,5,3,3,3,7,1,5,3,5,3,3,3,3,1,5,5,8,1,7,1,7,7
%N A304795 Number of positive special sums of the integer partition with Heinz number n.
%C A304795 A positive special sum of y is a number n > 0 such that exactly one submultiset of y sums to n. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A304795 Antti Karttunen, <a href="/A304795/b304795.txt">Table of n, a(n) for n = 1..65537</a>
%e A304795 The a(36) = 4 special sums are 1, 3, 5, 6, corresponding to the submultisets (1), (21), (221), (2211), with Heinz numbers 2, 6, 18, 36.
%t A304795 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A304795 uqsubs[y_]:=Join@@Select[GatherBy[Union[Rest[Subsets[y]]],Total],Length[#]===1&];
%t A304795 Table[Length[uqsubs[primeMS[n]]],{n,100}]
%o A304795 (PARI)
%o A304795 up_to = 65537;
%o A304795 A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
%o A304795 v056239 = vector(up_to,n,A056239(n));
%o A304795 A304795(n) = { my(m=Map(),s,k=0,c); fordiv(n,d,if(!mapisdefined(m,s = v056239[d],&c), mapput(m,s,1), mapput(m,s,c+1))); sumdiv(n,d,(1==mapget(m,v056239[d])))-1; }; \\ _Antti Karttunen_, Jul 02 2018
%Y A304795 Cf. A000712, A056239, A108917, A122768, A276024, A284640, A296150, A299701, A299702, A301854, A301855, A301957, A304793, A304796.
%K A304795 nonn
%O A304795 1,4
%A A304795 _Gus Wiseman_, May 18 2018
%E A304795 More terms from _Antti Karttunen_, Jul 02 2018