cp's OEIS Frontend

A380345 a(n) = n + sum of prime indices of n.

%I A380345 #5 Jan 26 2025 09:13:00
%S A380345 1,3,5,6,8,9,11,11,13,14,16,16,19,19,20,20,24,23,27,25,27,28,32,29,31,
%T A380345 33,33,34,39,36,42,37,40,42,42,42,49,47,47,46,54,49,57,51,52,56,62,54,
%U A380345 57,57,60,60,69,61,63,63,67,69,76,67,79,74,71,70,74,74,86
%N A380345 a(n) = n + sum of prime indices of n.
%C A380345 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, with sum A056239.
%F A380345 a(n) = n + A056239(n).
%e A380345 72 has prime indices {1,1,1,2,2}, so a(72) = 72 + 7 = 79.
%t A380345 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A380345 Table[n+Total[prix[n]],{n,100}]
%Y A380345 For factors instead of indices we have A075254.
%Y A380345 For minus instead of plus we have A178503.
%Y A380345 Triangles:
%Y A380345 - A027746 = prime factors
%Y A380345 - A112798 = prime indices
%Y A380345 Statistics:
%Y A380345 - A000027 = product of prime factors = row products of A027746
%Y A380345 - A001414 = sum of prime factors = row sums of A027746
%Y A380345 - A003963 = product of prime indices = row products of A112798
%Y A380345 - A056239 = sum of prime indices = row sums of A112798
%Y A380345 Combinations:
%Y A380345 - A075254 = product of factors + sum of factors = A000027 + A001414
%Y A380345 - A075255 = product of factors - sum of factors = A000027 - A001414
%Y A380345 - A178503 = product of factors - sum of indices = A000027 - A056239
%Y A380345 - A325036 = product of indices - sum of indices = A003963 - A056239
%Y A380345 - A379681 = product of indices + sum of indices = A003963 + A056239
%Y A380345 - A380344 = product of indices - sum of factors = A003963 - A001414
%Y A380345 - A380345 = product of factors + sum of indices = A000027 + A056239
%Y A380345 - A380409 = product of indices + sum of factors = A003963 + A001414
%Y A380345 A000040 lists the primes, differences A001223.
%Y A380345 A001222 counts prime factors with multiplicity.
%Y A380345 A055396 gives least prime index, greatest A061395.
%Y A380345 Cf. A000720, A175508, A319000, A325032, A325033, A325034, A325035, A325040, A331384, A379682, A380220.
%K A380345 nonn
%O A380345 1,2
%A A380345 _Gus Wiseman_, Jan 25 2025