cp's OEIS Frontend

A357485 Heinz numbers of integer partitions with the same length as reverse-alternating sum.

%I A357485 #6 Oct 02 2022 10:33:45
%S A357485 1,2,20,42,45,105,110,125,176,182,231,245,312,374,396,429,494,605,663,
%T A357485 680,702,780,782,845,891,969,1064,1088,1100,1102,1311,1426,1428,1445,
%U A357485 1530,1755,1805,1820,1824,1950,2001,2024,2146,2156,2394,2448,2475,2508,2542
%N A357485 Heinz numbers of integer partitions with the same length as reverse-alternating sum.
%C A357485 The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
%C A357485 The reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^i y_i.
%e A357485 The terms together with their prime indices begin:
%e A357485      1: {}
%e A357485      2: {1}
%e A357485     20: {1,1,3}
%e A357485     42: {1,2,4}
%e A357485     45: {2,2,3}
%e A357485    105: {2,3,4}
%e A357485    110: {1,3,5}
%e A357485    125: {3,3,3}
%e A357485    176: {1,1,1,1,5}
%e A357485    182: {1,4,6}
%e A357485    231: {2,4,5}
%e A357485    245: {3,4,4}
%e A357485    312: {1,1,1,2,6}
%e A357485    374: {1,5,7}
%e A357485    396: {1,1,2,2,5}
%t A357485 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A357485 ats[y_]:=Sum[(-1)^(i-1)*y[[i]],{i,Length[y]}];
%t A357485 Select[Range[100],PrimeOmega[#]==ats[primeMS[#]]&]
%Y A357485 The version for compositions is A357184, counted by A357182.
%Y A357485 These partitions are counted by A357189.
%Y A357485 For absolute value we have A357486, counted by A357487.
%Y A357485 A000041 counts partitions, strict A000009.
%Y A357485 A000712 up to 0's counts partitions w sum = twice alt sum, ranked A349159.
%Y A357485 A001055 counts partitions with product equal to sum, ranked by A301987.
%Y A357485 A006330 up to 0's counts partitions w sum = twice rev-alt sum, rank A349160.
%Y A357485 Cf. A004526, A025047, A051159, A131044, A262046, A357136.
%K A357485 nonn
%O A357485 1,2
%A A357485 _Gus Wiseman_, Oct 01 2022