cp's OEIS Frontend

A064939 a(n) = Sum_{i=1..omega(n)} i*p_i, where {p_i}, i=1..omega(n) is the increasing sequence of prime divisors of n, where omega is the number of distinct prime factors of n (A001221).

%I A064939 #21 Aug 22 2020 12:33:19
%S A064939 0,2,3,2,5,8,7,2,3,12,11,8,13,16,13,2,17,8,19,12,17,24,23,8,5,28,3,16,
%T A064939 29,23,31,2,25,36,19,8,37,40,29,12,41,29,43,24,13,48,47,8,7,12,37,28,
%U A064939 53,8,27,16,41,60,59,23,61,64,17,2,31,41,67,36,49,33,71,8,73,76,13,40
%N A064939 a(n) = Sum_{i=1..omega(n)} i*p_i, where {p_i}, i=1..omega(n) is the increasing sequence of prime divisors of n, where omega is the number of distinct prime factors of n (A001221).
%H A064939 Harry J. Smith, <a href="/A064939/b064939.txt">Table of n, a(n) for n = 1..1000</a>
%F A064939 a(n) = Sum_{p|n, q|n, p and q prime, p <= q} q. - _Wesley Ivan Hurt_, Aug 20 2020
%e A064939 factorset(30) = {2,3,5}, thus a(30) = 1*2 + 2*3 + 3*5 = 23.
%p A064939 with(numtheory): seq(add(i*sort(convert(factorset(n),'list'))[i],i=1..nops(factorset(n))), n=1..200);
%t A064939 ispd[n_]:=Module[{f=FactorInteger[n][[All,1]]},Total[f Range[ Length[f]]]]; Join[{0},Array[ispd,80,2]] (* _Harvey P. Dale_, Aug 06 2017 *)
%o A064939 (PARI) { for (n=1, 1000, f=factor(n)~; a=sum(i=1, length(f), i*f[1, i]); write("b064939.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 30 2009
%Y A064939 Cf. A001221 (omega).
%K A064939 nonn
%O A064939 1,2
%A A064939 _Vladeta Jovovic_, Oct 27 2001