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A325778 Heinz numbers of integer partitions whose distinct consecutive subsequences have different sums.

%I A325778 #5 May 21 2019 22:06:06
%S A325778 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,
%T A325778 29,31,32,33,34,35,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,
%U A325778 56,57,58,59,61,62,64,65,66,67,68,69,71,73,74,75,76,77
%N A325778 Heinz numbers of integer partitions whose distinct consecutive subsequences have different sums.
%C A325778 First differs from A299702 in having 462.
%C A325778 The enumeration of these partitions by sum is given by A325769.
%e A325778 Most small numbers are in the sequence. However, the sequence of non-terms together with their prime indices begins:
%e A325778   12: {1,1,2}
%e A325778   24: {1,1,1,2}
%e A325778   30: {1,2,3}
%e A325778   36: {1,1,2,2}
%e A325778   40: {1,1,1,3}
%e A325778   48: {1,1,1,1,2}
%e A325778   60: {1,1,2,3}
%e A325778   63: {2,2,4}
%e A325778   70: {1,3,4}
%e A325778   72: {1,1,1,2,2}
%e A325778   80: {1,1,1,1,3}
%e A325778   84: {1,1,2,4}
%e A325778   90: {1,2,2,3}
%e A325778   96: {1,1,1,1,1,2}
%t A325778 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325778 Select[Range[100],UnsameQ@@Total/@Union[ReplaceList[primeMS[#],{___,s__,___}:>{s}]]&]
%Y A325778 Complement of A325777.
%Y A325778 Cf. A002033, A056239, A112798, A143823, A169942, A299702, A301899, A325676, A325768, A325769, A325770, A325779.
%K A325778 nonn
%O A325778 1,2
%A A325778 _Gus Wiseman_, May 20 2019