cp's OEIS Frontend

A325043 Heinz numbers of integer partitions, with at least three parts, whose product of parts is one fewer than their sum.

%I A325043 #9 Jun 28 2020 02:25:36
%S A325043 18,60,168,216,400,528,1248,2240,2880,3264,7296,14080,17664,25088,
%T A325043 32256,41472,44544,66560,95232,153600,227328,315392,348160,405504,
%U A325043 503808,1056768,1556480,2310144,2981888,3833856,5210112,6881280,7536640,7929856,8847360,11599872
%N A325043 Heinz numbers of integer partitions, with at least three parts, whose product of parts is one fewer than their sum.
%C A325043 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are numbers with at least three prime factors (counted with multiplicity) whose product of prime indices (A003963) is one fewer than their sum of prime indices (A056239).
%F A325043 a(n) = 2 * A301988(n).
%e A325043 The sequence of terms together with their prime indices begins:
%e A325043      18: {1,2,2}
%e A325043      60: {1,1,2,3}
%e A325043     168: {1,1,1,2,4}
%e A325043     216: {1,1,1,2,2,2}
%e A325043     400: {1,1,1,1,3,3}
%e A325043     528: {1,1,1,1,2,5}
%e A325043    1248: {1,1,1,1,1,2,6}
%e A325043    2240: {1,1,1,1,1,1,3,4}
%e A325043    2880: {1,1,1,1,1,1,2,2,3}
%e A325043    3264: {1,1,1,1,1,1,2,7}
%e A325043    7296: {1,1,1,1,1,1,1,2,8}
%e A325043   14080: {1,1,1,1,1,1,1,1,3,5}
%e A325043   17664: {1,1,1,1,1,1,1,1,2,9}
%e A325043   25088: {1,1,1,1,1,1,1,1,1,4,4}
%e A325043   32256: {1,1,1,1,1,1,1,1,1,2,2,4}
%e A325043   41472: {1,1,1,1,1,1,1,1,1,2,2,2,2}
%e A325043   44544: {1,1,1,1,1,1,1,1,1,2,10}
%e A325043   66560: {1,1,1,1,1,1,1,1,1,1,3,6}
%e A325043   95232: {1,1,1,1,1,1,1,1,1,1,2,11}
%t A325043 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325043 Select[Range[10000],And[PrimeOmega[#]>2,Times@@primeMS[#]==Total[primeMS[#]]-1]&]
%Y A325043 Cf. A000720, A003963, A056239, A112798, A178503, A175508, A301987, A319000.
%Y A325043 Cf. A325032, A325033, A325036, A325037, A325038, A325041, A325042, A325044.
%K A325043 nonn
%O A325043 1,1
%A A325043 _Gus Wiseman_, Mar 25 2019
%E A325043 More terms from _Jinyuan Wang_, Jun 27 2020