cp's OEIS Frontend

A366839 Sum of even prime factors of 2n, counted with multiplicity.

%I A366839 #13 Sep 13 2024 06:56:58
%S A366839 2,4,2,6,2,4,2,8,2,4,2,6,2,4,2,10,2,4,2,6,2,4,2,8,2,4,2,6,2,4,2,12,2,
%T A366839 4,2,6,2,4,2,8,2,4,2,6,2,4,2,10,2,4,2,6,2,4,2,8,2,4,2,6,2,4,2,14,2,4,
%U A366839 2,6,2,4,2,8,2,4,2,6,2,4,2,10,2,4,2,6,2
%N A366839 Sum of even prime factors of 2n, counted with multiplicity.
%F A366839 a(n) = 2*A001511(n).
%F A366839 a(n) = A100006(n) - A366840(2n).
%F A366839 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4. - _Amiram Eldar_, Sep 13 2024
%e A366839 The prime factors of 2*60 are {2,2,2,3,5}, of which the even factors are {2,2,2}, so a(60) = 6.
%t A366839 Table[2*Length[NestWhileList[#/2&,n,EvenQ]],{n,100}]
%o A366839 (PARI) a(n) = 2 * valuation(n, 2) + 2; \\ _Amiram Eldar_, Sep 13 2024
%Y A366839 A compound version is A001414, triangle A331416.
%Y A366839 Dividing by 2 gives A001511.
%Y A366839 Positions of 2's are A005408.
%Y A366839 For count instead of sum we have A007814, odd version A087436.
%Y A366839 The partition triangle for this statistic is A116598 aerated.
%Y A366839 For indices we have A366531, halved A366533, triangle A113686/A174713.
%Y A366839 The odd version is A366840.
%Y A366839 A019507 lists numbers with (even factor sum) = (odd factor sum).
%Y A366839 A066207 lists numbers with all even prime indices, counted by A035363.
%Y A366839 A112798 lists prime indices, reverse A296150, length A001222, sum A056239.
%Y A366839 A162641 counts even prime exponents, odd A162642.
%Y A366839 A239261 counts partitions with (sum of odd parts) = (sum of even parts).
%Y A366839 A257992 counts even prime indices, odd A257991.
%Y A366839 A366528 adds up odd prime indices, triangle A113685 (without zeros A365067).
%Y A366839 Cf. A000720, A066208, A258117, A325698.
%K A366839 nonn
%O A366839 1,1
%A A366839 _Gus Wiseman_, Oct 25 2023