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A325706 Heinz numbers of integer partitions containing all of their distinct multiplicities.

%I A325706 #5 May 18 2019 22:46:36
%S A325706 1,2,6,9,10,12,14,18,22,26,30,34,36,38,40,42,46,58,60,62,66,70,74,78,
%T A325706 82,84,86,90,94,102,106,110,112,114,118,120,122,125,126,130,132,134,
%U A325706 138,142,146,150,154,156,158,166,170,174,178,180,182,186,190,194,198
%N A325706 Heinz numbers of integer partitions containing all of their distinct multiplicities.
%C A325706 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325706 Also numbers n divisible by the squarefree kernel of their "shadow" A181819(n).
%C A325706 The enumeration of these partitions by sum is given by A325705.
%e A325706 The sequence of terms together with their prime indices begins:
%e A325706     1: {}
%e A325706     2: {1}
%e A325706     6: {1,2}
%e A325706     9: {2,2}
%e A325706    10: {1,3}
%e A325706    12: {1,1,2}
%e A325706    14: {1,4}
%e A325706    18: {1,2,2}
%e A325706    22: {1,5}
%e A325706    26: {1,6}
%e A325706    30: {1,2,3}
%e A325706    34: {1,7}
%e A325706    36: {1,1,2,2}
%e A325706    38: {1,8}
%e A325706    40: {1,1,1,3}
%e A325706    42: {1,2,4}
%e A325706    46: {1,9}
%e A325706    58: {1,10}
%e A325706    60: {1,1,2,3}
%e A325706    62: {1,11}
%t A325706 Select[Range[100],#==1||SubsetQ[PrimePi/@First/@FactorInteger[#],Last/@FactorInteger[#]]&]
%Y A325706 Cf. A056239, A109297, A112798, A114639, A114640, A181819, A225486, A290689, A324753, A324843, A325702, A325705, A325707, A325755.
%K A325706 nonn
%O A325706 1,2
%A A325706 _Gus Wiseman_, May 18 2019