cp's OEIS Frontend

A358102 Numbers of the form prime(w)*prime(x)*prime(y) with w >= x >= y such that 2w = 3x + 4y.

%I A358102 #8 Nov 02 2022 11:54:09
%S A358102 66,153,266,609,806,1295,1599,1634,2107,3021,3055,3422,5254,5369,5795,
%T A358102 5829,7138,8769,9443,9581,10585,10706,12337,12513,13298,16465,16511,
%U A358102 16849,17013,18602,21983,22145,23241,23542,26159,29014,29607,29945,30943,32623,32809
%N A358102 Numbers of the form prime(w)*prime(x)*prime(y) with w >= x >= y such that 2w = 3x + 4y.
%C A358102 Also Heinz numbers of integer partitions (w,x,y) summing to n such that 2w = 3x + 4y, where the Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A358102 The terms together with their prime indices begin:
%e A358102      66: {1,2,5}
%e A358102     153: {2,2,7}
%e A358102     266: {1,4,8}
%e A358102     609: {2,4,10}
%e A358102     806: {1,6,11}
%e A358102    1295: {3,4,12}
%e A358102    1599: {2,6,13}
%e A358102    1634: {1,8,14}
%e A358102    2107: {4,4,14}
%e A358102    3021: {2,8,16}
%e A358102    3055: {3,6,15}
%e A358102    3422: {1,10,17}
%e A358102    5254: {1,12,20}
%e A358102    5369: {4,6,17}
%e A358102    5795: {3,8,18}
%e A358102    5829: {2,10,19}
%e A358102    7138: {1,14,23}
%e A358102    8769: {2,12,22}
%t A358102 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358102 Select[Range[1000],PrimeOmega[#]==3&&2*primeMS[#][[-1]]==3*primeMS[#][[-2]]+4*primeMS[#][[-3]]&]
%Y A358102 The ordered version is A357489, apparently counted by A008676.
%Y A358102 These partitions are counted by A357849.
%Y A358102 A000040 lists the primes.
%Y A358102 A000041 counts partitions, strict A000009.
%Y A358102 A003963 multiplies prime indices.
%Y A358102 A056239 adds up prime indices.
%Y A358102 Cf. A000720, A001221, A001222, A215366, A296150, A318283.
%K A358102 nonn
%O A358102 1,1
%A A358102 _Gus Wiseman_, Nov 02 2022