cp's OEIS Frontend

A335403 If n = Product_{i=1..k} p_i^e_i then a(n) = Sum_{i=1..k} e_i * prime(p_i).

%I A335403 #17 Jun 20 2020 00:13:06
%S A335403 0,3,5,6,11,8,17,9,10,14,31,11,41,20,16,12,59,13,67,17,22,34,83,14,22,
%T A335403 44,15,23,109,19,127,15,36,62,28,16,157,70,46,20,179,25,191,37,21,86,
%U A335403 211,17,34,25,64,47,241,18,42,26,72,112,277,22,283,130,27,18
%N A335403 If n = Product_{i=1..k} p_i^e_i then a(n) = Sum_{i=1..k} e_i * prime(p_i).
%C A335403 Totally additive with a(p) = prime(p) for p prime.
%H A335403 Wikipedia, <a href="https://en.wikipedia.org/wiki/Additive_function">Additive function</a>
%e A335403 The prime factors of 18 are 2 * 3 * 3, so a(18) = prime(2) + prime(3) + prime(3) = 13.
%t A335403 Table[Total[Cases[FactorInteger[n],{p_,k_}:>k*Prime[p]]],{n,30}]
%o A335403 (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, prime(f[k,1])*f[k,2]); \\ _Michel Marcus_, Jun 07 2020
%Y A335403 Partitions into prime parts are A000607.
%Y A335403 Sum of prime factors is A001414.
%Y A335403 Primes of prime index are A006450.
%Y A335403 Sum of prime indices is A056239.
%Y A335403 The multiplicative version is A064988.
%Y A335403 Products of primes of prime index are A076610.
%Y A335403 Numbers whose prime indices are not all prime are A330945.
%Y A335403 Cf. A000040, A000720, A001222, A003961, A003963, A007097, A112798, A178503, A257994, A302242, A324851, A331915.
%K A335403 nonn,look
%O A335403 1,2
%A A335403 _Gus Wiseman_, Jun 06 2020
%E A335403 Edited by _N. J. A. Sloane_, Jun 20 2020 following a suggestion from _Bernard Schott_.