cp's OEIS Frontend

A366737 Number of numbers k <= A056239(n) that can be written as a linear combination of the prime indices of n (allowing coefficients of 0).

%I A366737 #10 Oct 20 2023 01:51:27
%S A366737 0,1,1,2,1,3,1,3,2,4,1,4,1,5,4,4,1,5,1,5,3,6,1,5,2,7,3,6,1,6,1,5,5,8,
%T A366737 4,6,1,9,4,6,1,7,1,7,6,10,1,6,2,7,6,8,1,7,4,7,5,11,1,7,1,12,4,6,3,8,1,
%U A366737 9,7,8,1,7,1,13,7,10,4,9,1,7,4,14,1,8,5
%N A366737 Number of numbers k <= A056239(n) that can be written as a linear combination of the prime indices of n (allowing coefficients of 0).
%C A366737 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%F A366737 a(2n) = A056239(2n) - 1 for n > 0.
%e A366737 The prime indices of 33 are {2,5}, with combinations
%e A366737   2 = 2
%e A366737   4 = 2+2
%e A366737   5 = 5
%e A366737   6 = 2+2+2
%e A366737   7 = 5+2
%e A366737 Hence a(33) = 5.
%t A366737 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A366737 combs[n_,y_]:=With[{s=Table[{k,i},{k,y},{i,0,Floor[n/k]}]},Select[Tuples[s],Total[Times@@@#]==n&]];
%t A366737 Table[Length[Select[Range[Total[prix[n]]],combs[#,prix[n]]!={}&]],{n,30}]
%Y A366737 For minimum instead of length we have A055396.
%Y A366737 Positions of first appearances are 1, 2, and A100484.
%Y A366737 For subsets instead of combinations we have A304793, complement A325799.
%Y A366737 A056239 adds up prime indices, row sums of A112798.
%Y A366737 A126796 counts complete partitions, ranks A325781, strict A188431.
%Y A366737 A276024 counts positive subset-sums of partitions, strict A284640.
%Y A366737 A365924 counts incomplete partitions, ranks A365830, strict A365831.
%Y A366737 Cf. A018818, A046663, A055932, A299701, A365658, A365918, A365921.
%K A366737 nonn
%O A366737 1,4
%A A366737 _Gus Wiseman_, Oct 19 2023