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%I #8 Apr 13 2019 09:01:27
%S 1,2,4,7,8,14,16,23,28,32,46,49,53,56,64,92,97,98,106,112,128,151,161,
%T 184,194,196,212,224,227,256,302,311,322,343,368,371,388,392,419,424,
%U 448,454,512,529,541,604,622,644,661,679,686,736,742,776,784,827,838
%N Heinz numbers of integer partitions of n into perfect squares (A001156).
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C Also products of elements of A011757.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 4: {1,1}
%e 7: {4}
%e 8: {1,1,1}
%e 14: {1,4}
%e 16: {1,1,1,1}
%e 23: {9}
%e 28: {1,1,4}
%e 32: {1,1,1,1,1}
%e 46: {1,9}
%e 49: {4,4}
%e 53: {16}
%e 56: {1,1,1,4}
%e 64: {1,1,1,1,1,1}
%e 92: {1,1,9}
%e 97: {25}
%e 98: {1,4,4}
%t Select[Range[100],And@@Cases[FactorInteger[#],{p_,_}:>IntegerQ[Sqrt[PrimePi[p]]]]&]
%Y Cf. A001156, A011757, A033461, A052335, A056239, A062457, A078135, A112798, A117144, A118914, A276078.
%Y Cf. A109298, A324524, A324525, A324571, A324572, A324587.
%K nonn
%O 1,2
%A _Gus Wiseman_, Mar 08 2019
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