A319334 - OEIS

%I #5 Sep 19 2018 09:17:30

%S 30,198,264,273,364,490,525,630,700,840,918,1120,1224,1495,1632,1794,

%T 2392,2420,2750,3105,3450,3726,4140,4263,4400,4466,4921,4968,5481,

%U 5520,5684,6327,6624,7030,7040,7308,8436,8832,9744,11248,12992,14079,14450,14993

%N Nonprime Heinz numbers of integer partitions whose sum is equal to their LCM.

%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

%e The sequence of all non-singleton integer partitions whose sum is equal to their LCM begins: (321), (5221), (52111), (642), (6411), (4431), (4332), (43221), (43311), (432111), (72221), (4311111), (722111), (963), (7211111), (9621).

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[2,1000],And[!PrimeQ[#],LCM@@primeMS[#]==Total[primeMS[#]]]&]

%Y Cf. A067538, A074761, A143773, A290103, A305566, A316429, A316431, A316432, A316433, A317624, A319315, A319333.

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 17 2018