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.
%I A340931 #5 Feb 07 2021 19:43:35
%S A340931 2,5,8,11,17,18,20,23,31,32,41,42,44,45,47,50,59,67,68,72,73,78,80,83,
%T A340931 92,97,98,99,103,105,109,110,114,124,125,127,128,137,149,153,157,162,
%U A340931 164,167,168,170,174,176,179,180,182,188,191,195,197,200,207,211
%N A340931 Heinz numbers of integer partitions of odd numbers into an odd number of parts.
%C A340931 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This is a bijective correspondence between positive integers and integer partitions.
%F A340931 Intersection of A026424 and A300063.
%e A340931 The sequence of terms together with the corresponding partitions begins:
%e A340931 2: (1) 50: (3,3,1) 109: (29)
%e A340931 5: (3) 59: (17) 110: (5,3,1)
%e A340931 8: (1,1,1) 67: (19) 114: (8,2,1)
%e A340931 11: (5) 68: (7,1,1) 124: (11,1,1)
%e A340931 17: (7) 72: (2,2,1,1,1) 125: (3,3,3)
%e A340931 18: (2,2,1) 73: (21) 127: (31)
%e A340931 20: (3,1,1) 78: (6,2,1) 128: (1,1,1,1,1,1,1)
%e A340931 23: (9) 80: (3,1,1,1,1) 137: (33)
%e A340931 31: (11) 83: (23) 149: (35)
%e A340931 32: (1,1,1,1,1) 92: (9,1,1) 153: (7,2,2)
%e A340931 41: (13) 97: (25) 157: (37)
%e A340931 42: (4,2,1) 98: (4,4,1) 162: (2,2,2,2,1)
%e A340931 44: (5,1,1) 99: (5,2,2) 164: (13,1,1)
%e A340931 45: (3,2,2) 103: (27) 167: (39)
%e A340931 47: (15) 105: (4,3,2) 168: (4,2,1,1,1)
%t A340931 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A340931 Select[Range[100],OddQ[PrimeOmega[#]]&&OddQ[Total[primeMS[#]]]&]
%Y A340931 Note: A-numbers of Heinz-number sequences are in parentheses below.
%Y A340931 These partitions are counted by A160786.
%Y A340931 The even version is A236913 (A340784).
%Y A340931 The case of where the prime indices are also odd is A300272.
%Y A340931 A000009 counts partitions into odd parts (A066208).
%Y A340931 A001222 counts prime factors.
%Y A340931 A027193 counts odd-length partitions (A026424).
%Y A340931 A047993 counts balanced partitions (A106529).
%Y A340931 A056239 adds up prime indices.
%Y A340931 A058695 counts partitions of odd numbers (A300063).
%Y A340931 A072233 counts partitions by sum and length.
%Y A340931 A112798 lists the prime indices of each positive integer.
%Y A340931 Cf. A000041, A316413, A326845, A340385, A340386, A340387, A340604, A340607, A340854, A340855.
%K A340931 nonn
%O A340931 1,1
%A A340931 _Gus Wiseman_, Feb 05 2021