cp's OEIS Frontend

A324588 Heinz numbers of integer partitions of n into perfect squares (A001156).

%I A324588 #8 Apr 13 2019 09:01:27
%S A324588 1,2,4,7,8,14,16,23,28,32,46,49,53,56,64,92,97,98,106,112,128,151,161,
%T A324588 184,194,196,212,224,227,256,302,311,322,343,368,371,388,392,419,424,
%U A324588 448,454,512,529,541,604,622,644,661,679,686,736,742,776,784,827,838
%N A324588 Heinz numbers of integer partitions of n into perfect squares (A001156).
%C A324588 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A324588 Also products of elements of A011757.
%e A324588 The sequence of terms together with their prime indices begins:
%e A324588    1: {}
%e A324588    2: {1}
%e A324588    4: {1,1}
%e A324588    7: {4}
%e A324588    8: {1,1,1}
%e A324588   14: {1,4}
%e A324588   16: {1,1,1,1}
%e A324588   23: {9}
%e A324588   28: {1,1,4}
%e A324588   32: {1,1,1,1,1}
%e A324588   46: {1,9}
%e A324588   49: {4,4}
%e A324588   53: {16}
%e A324588   56: {1,1,1,4}
%e A324588   64: {1,1,1,1,1,1}
%e A324588   92: {1,1,9}
%e A324588   97: {25}
%e A324588   98: {1,4,4}
%t A324588 Select[Range[100],And@@Cases[FactorInteger[#],{p_,_}:>IntegerQ[Sqrt[PrimePi[p]]]]&]
%Y A324588 Cf. A001156, A011757, A033461, A052335, A056239, A062457, A078135, A112798, A117144, A118914, A276078.
%Y A324588 Cf. A109298, A324524, A324525, A324571, A324572, A324587.
%K A324588 nonn
%O A324588 1,2
%A A324588 _Gus Wiseman_, Mar 08 2019