cp's OEIS Frontend

A366840 Sum of odd prime factors of n, counted with multiplicity.

%I A366840 #16 Nov 03 2023 08:03:21
%S A366840 0,0,3,0,5,3,7,0,6,5,11,3,13,7,8,0,17,6,19,5,10,11,23,3,10,13,9,7,29,
%T A366840 8,31,0,14,17,12,6,37,19,16,5,41,10,43,11,11,23,47,3,14,10,20,13,53,9,
%U A366840 16,7,22,29,59,8,61,31,13,0,18,14,67,17,26,12,71,6
%N A366840 Sum of odd prime factors of n, counted with multiplicity.
%C A366840 Contains all positive integers except 1, 2, 4.
%F A366840 a(n) = A100006(n) - A366839(n).
%F A366840 a(2n) = a(n).
%F A366840 a(2n-1) = A001414(2n-1) = A100005(n).
%F A366840 Completely additive with a(2^e) = 0 and a(p^e) = e*p for an odd prime p. - _Amiram Eldar_, Nov 03 2023
%e A366840 The prime factors of 60 are {2,2,2,3,5}, of which the odd factors are {3,5}, so a(60) = 8.
%t A366840 Table[Total[Times@@@DeleteCases[If[n==1,{}, FactorInteger[n]],{2,_}]],{n,100}]
%o A366840 (PARI) a(n) = my(f=factor(n), j=if(n%2, 1, 2)); sum(i=j, #f~, f[i,1]*f[i,2]); \\ _Michel Marcus_, Oct 30 2023
%Y A366840 The compound version is A001414, triangle A331416.
%Y A366840 For count instead of sum we have A087436, even version A007814.
%Y A366840 Odd-indexed terms are A100005.
%Y A366840 Positions of odd terms are A335657, even A036349.
%Y A366840 For prime indices we have A366528, triangle A113685 (without zeros A365067)
%Y A366840 The even version is A366839 = 2*A001511.
%Y A366840 The partition triangle for this statistic is A366851, even version A116598.
%Y A366840 A019507 lists numbers with (even factor sum) = (odd factor sum).
%Y A366840 A066207 lists numbers with all even prime indices, counted by A035363.
%Y A366840 A112798 lists prime indices, reverse A296150, length A001222, sum A056239.
%Y A366840 A162641 counts even prime exponents, odd A162642.
%Y A366840 A239261 counts partitions with (sum of odd parts) = (sum of even parts).
%Y A366840 A257992 counts even prime indices, odd A257991.
%Y A366840 Cf. A000009, A066208, A113686, A174713, A258117, A325698, A366531, A366850.
%K A366840 nonn,easy
%O A366840 1,3
%A A366840 _Gus Wiseman_, Oct 27 2023