cp's OEIS Frontend

A379682 Least number whose prime indices have sum + product = n.

%I A379682 #5 Jan 05 2025 22:34:58
%S A379682 1,2,4,3,6,5,10,7,14,11,15,13,26,17,25,19,33,23,35,29,58,31,51,37,74,
%T A379682 41,65,43,69,47,85,53,105,59,93,61,122,67,115,71,123,73,145,79,158,83,
%U A379682 141,89,161,97,185,101,177,103,205,107,214,109,201,113,226,127
%N A379682 Least number whose prime indices have sum + product = n.
%C A379682 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.
%e A379682 The positions of 11 in A379681 are: 15, 22, 56, 72, 160, 384, 1024, so a(11) = 15.
%t A379682 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A379682 sp=Table[Plus@@prix[n]+Times@@prix[n],{n,1000}];
%t A379682 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A379682 Table[Position[sp,n][[1,1]],{n,mnrm[sp]}]
%Y A379682 Position of first appearance of n in A379681.
%Y A379682 The subtraction A325036 takes the following values:
%Y A379682 - zero: A301987, counted by A001055
%Y A379682 - negative: A325037, counted by A114324
%Y A379682 - positive: A325038, counted by A096276 shifted right
%Y A379682 - negative one: A325041, counted by A028422
%Y A379682 - one: A325042, counted by A001055 shifted right
%Y A379682 - nonnegative: A325044, counted by A096276
%Y A379682 - nonpositive: A379721, counted by A319005
%Y A379682 A000040 lists the primes, differences A001223.
%Y A379682 A055396 gives least prime index, greatest A061395.
%Y A379682 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A379682 Cf. A000720, A003963, A075254, A178503, A175508, A319000, A325032, A325033, A325034, A325035, A325040.
%K A379682 nonn
%O A379682 1,2
%A A379682 _Gus Wiseman_, Jan 05 2025