cp's OEIS Frontend

A358137 Heinz number of the partial sums of the prime indices of n.

%I A358137 #9 Jan 02 2023 15:26:06
%S A358137 1,2,3,6,5,10,7,30,21,14,11,42,13,22,33,210,17,110,19,66,39,26,23,330,
%T A358137 65,34,273,78,29,130,31,2310,51,38,85,546,37,46,57,390,41,170,43,102,
%U A358137 357,58,47,2730,133,238,69,114,53,1870,95,510,87,62,59,714,61
%N A358137 Heinz number of the partial sums of the prime indices of n.
%C A358137 The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
%F A358137 A001222(a(n)) = A001222(n).
%e A358137 The terms together with their prime indices begin:
%e A358137       1: {}
%e A358137       2: {1}
%e A358137       3: {2}
%e A358137       6: {1,2}
%e A358137       5: {3}
%e A358137      10: {1,3}
%e A358137       7: {4}
%e A358137      30: {1,2,3}
%e A358137      21: {2,4}
%e A358137      14: {1,4}
%e A358137      11: {5}
%e A358137      42: {1,2,4}
%e A358137      13: {6}
%e A358137      22: {1,5}
%e A358137      33: {2,5}
%e A358137     210: {1,2,3,4}
%e A358137      17: {7}
%e A358137     110: {1,3,5}
%t A358137 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358137 Table[Times@@Prime/@Accumulate[primeMS[n]],{n,100}]
%Y A358137 The sorted version is A325362.
%Y A358137 The prime indices are rows of A358136, partial sums of rows of A112798.
%Y A358137 A000040 lists the primes.
%Y A358137 A000041 counts partitions, strict A000009.
%Y A358137 A003963 multiplies prime indices.
%Y A358137 A056239 adds up prime indices.
%Y A358137 Cf. A000720, A001221, A001222, A215366, A296150, A318283, A355536, A358134.
%K A358137 nonn
%O A358137 1,2
%A A358137 _Gus Wiseman_, Oct 31 2022