cp's OEIS Frontend

A349909 Partial sums of A347870; Number of terms of A347877 (numbers k with an odd arithmetic derivative of sigma(k)) in range 1..n.

%I A349909 #6 Feb 14 2022 11:21:30
%S A349909 0,1,1,2,3,3,3,3,4,5,5,5,6,6,6,7,8,8,8,9,9,9,9,9,10,11,11,11,12,12,12,
%T A349909 13,13,14,14,14,15,15,15,16,17,17,17,17,18,18,18,18,18,18,18,19,20,20,
%U A349909 20,20,20,21,21,21,22,22,22,23,23,23,23,24,24,24,24,25,26,27,27,27,27,27,27,28,28,29,29,29,29
%N A349909 Partial sums of A347870; Number of terms of A347877 (numbers k with an odd arithmetic derivative of sigma(k)) in range 1..n.
%C A349909 Density of terms of A347877 in N seem to be steadily decreasing, e.g. for a(8)/8 = 3/8 = 0.375, a(1024)/1024 = 249/1024 = 0.243..., and a(2^20)/2^20 = 117216/1048576 = 0.111786...
%F A349909 a(1) = 0; for n > 1, a(n) = A347870(n) + a(n-1).
%F A349909 For all n >= 1, a(A347877(n)) = n.
%o A349909 (PARI)
%o A349909 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A349909 A342925(n) = A003415(sigma(n));
%o A349909 A347870(n) = (A342925(n)%2);
%o A349909 A349909(n) = if(1==n,A347870(n),A347870(n)+A349909(n-1));
%Y A349909 Cf. A000203, A003415, A342925, A347870, A347877, A349909.
%K A349909 nonn
%O A349909 1,4
%A A349909 _Antti Karttunen_, Feb 13 2022