cp's OEIS Frontend

A341885 a(n) is the sum of A000217(p) over the prime factors p of n, counted with multiplicity.

%I A341885 #24 May 22 2025 21:01:31
%S A341885 0,3,6,6,15,9,28,9,12,18,66,12,91,31,21,12,153,15,190,21,34,69,276,15,
%T A341885 30,94,18,34,435,24,496,15,72,156,43,18,703,193,97,24,861,37,946,72,
%U A341885 27,279,1128,18,56,33,159,97,1431,21,81,37,196,438,1770,27,1891,499,40,18,106,75,2278,159,282
%N A341885 a(n) is the sum of A000217(p) over the prime factors p of n, counted with multiplicity.
%C A341885 By definition, this sequence is completely additive. - _Peter Munn_, Aug 14 2022
%H A341885 Robert Israel, <a href="/A341885/b341885.txt">Table of n, a(n) for n = 1..10000</a>
%e A341885 18 = 2*3*3 so a(18) = 2*3/2 + 3*4/2 + 3*4/2 = 15.
%p A341885 f:= proc(n) local t; add(t[1]*(t[1]+1)/2*t[2], t = ifactors(n)[2]) end proc:
%p A341885 map(f, [$1..100]);
%t A341885 Prepend[Array[Total@ PolygonalNumber@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]] &, 68, 2], 0] (* _Michael De Vlieger_, Feb 22 2021 *)
%o A341885 (Python)
%o A341885 from sympy import factorint
%o A341885 def A341885(n): return sum(k*m*(m+1)//2 for m,k in factorint(n).items()) # _Chai Wah Wu_, Feb 25 2021
%o A341885 (PARI) a(n) = my(f=factor(n), p); sum(k=1, #f~, p=f[k,1]; f[k,2]*p*(p+1)/2); \\ _Michel Marcus_, Aug 14 2022
%Y A341885 Cf. A000217, A340834.
%Y A341885 For other completely additive sequences with primes p mapped to a function of p, see A001414.
%K A341885 nonn,easy
%O A341885 1,2
%A A341885 _J. M. Bergot_ and _Robert Israel_, Feb 22 2021