cp's OEIS Frontend

A379681 Sum plus product of the multiset of prime indices of n.

%I A379681 #6 Jan 05 2025 22:35:07
%S A379681 1,2,4,3,6,5,8,4,8,7,10,6,12,9,11,5,14,9,16,8,14,11,18,7,15,13,14,10,
%T A379681 20,12,22,6,17,15,19,10,24,17,20,9,26,15,28,12,19,19,30,8,24,16,23,14,
%U A379681 32,15,23,11,26,21,34,13,36,23,24,7,27,18,38,16,29,20
%N A379681 Sum plus product of the multiset of prime indices of n.
%C A379681 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.
%C A379681 Includes all positive integers.
%F A379681 a(n) = A056239(n) + A003963(n).
%F A379681 The last position of k is 2^(k-1).
%t A379681 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A379681 Table[Plus@@prix[n]+Times@@prix[n],{n,30}]
%Y A379681 For prime factors instead of indices we have A075254, subtracted A075255.
%Y A379681 Positions of first appearances are A379682.
%Y A379681 For minus instead of plus we have A325036, which takes the following values:
%Y A379681 - zero: A301987, counted by A001055
%Y A379681 - negative: A325037, counted by A114324
%Y A379681 - positive: A325038, counted by A096276 shifted right
%Y A379681 - negative one: A325041, counted by A028422
%Y A379681 - one: A325042, counted by A001055 shifted right
%Y A379681 - nonnegative: A325044, counted by A096276
%Y A379681 - nonpositive: A379721, counted by A319005
%Y A379681 A000040 lists the primes, differences A001223.
%Y A379681 A055396 gives least prime index, greatest A061395.
%Y A379681 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A379681 Cf. A000720, A003963, A178503, A175508, A319000, A325032, A325033, A325034, A325035, A325040.
%K A379681 nonn
%O A379681 1,2
%A A379681 _Gus Wiseman_, Jan 05 2025