cp's OEIS Frontend

A325779 Heinz numbers of integer partitions for which every restriction to a subinterval has a different sum.

%I A325779 #5 May 21 2019 22:06:12
%S A325779 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,31,33,34,35,37,38,39,
%T A325779 41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,71,73,74,77,78,79,
%U A325779 82,83,85,86,87,89,91,93,94,95,97,101,102,103,105,106,107
%N A325779 Heinz numbers of integer partitions for which every restriction to a subinterval has a different sum.
%C A325779 First differs from A301899 in having 462.
%C A325779 The enumeration of these partitions by sum is given by A325768.
%e A325779 Most small numbers are in the sequence. However, the sequence of non-terms together with their prime indices begins:
%e A325779     4: {1,1}
%e A325779     8: {1,1,1}
%e A325779     9: {2,2}
%e A325779    12: {1,1,2}
%e A325779    16: {1,1,1,1}
%e A325779    18: {1,2,2}
%e A325779    20: {1,1,3}
%e A325779    24: {1,1,1,2}
%e A325779    25: {3,3}
%e A325779    27: {2,2,2}
%e A325779    28: {1,1,4}
%e A325779    30: {1,2,3}
%e A325779    32: {1,1,1,1,1}
%e A325779    36: {1,1,2,2}
%e A325779    40: {1,1,1,3}
%e A325779    44: {1,1,5}
%e A325779    45: {2,2,3}
%e A325779    48: {1,1,1,1,2}
%e A325779    49: {4,4}
%e A325779    50: {1,3,3}
%t A325779 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325779 Select[Range[100],UnsameQ@@ReplaceList[primeMS[#],{___,s__,___}:>Plus[s]]&]
%Y A325779 A subsequence of A005117.
%Y A325779 Cf. A000041, A002033, A056239, A103300, A112798, A143823, A169942, A299702, A301899, A325676, A325768, A325769, A325770, A325778.
%K A325779 nonn
%O A325779 1,2
%A A325779 _Gus Wiseman_, May 20 2019