A325129 - OEIS

%I #4 Apr 01 2019 07:24:50

%S 1,3,5,9,11,13,15,17,19,25,27,29,31,33,37,39,41,43,45,47,51,55,57,59,

%T 61,65,67,71,73,75,79,81,83,85,87,89,93,95,99,101,103,107,109,111,113,

%U 117,121,123,125,127,129,131,135,137,139,141,143,145,149,153,155

%N Heinz numbers of integer partitions into nonsquares (A087153).

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

%e The sequence of terms together with their prime indices begins:

%e    1: {}

%e    3: {2}

%e    5: {3}

%e    9: {2,2}

%e   11: {5}

%e   13: {6}

%e   15: {2,3}

%e   17: {7}

%e   19: {8}

%e   25: {3,3}

%e   27: {2,2,2}

%e   29: {10}

%e   31: {11}

%e   33: {2,5}

%e   37: {12}

%e   39: {2,6}

%e   41: {13}

%e   43: {14}

%e   45: {2,2,3}

%t Select[Range[100],!MemberQ[If[#==1,{},FactorInteger[#]],{p_,_}/;IntegerQ[Sqrt[PrimePi[p]]]]&]

%Y Cf. A001156, A011757, A033461, A056239, A062457, A066328, A087153, A112798.

%Y Cf. A324571, A324587, A324588, A325128, A325130.

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 01 2019