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

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, 13, 13, 14, 14, 14, 15, 15, 15, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 19, 20, 20, 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

Offset

1,4

Comments

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...

Links

Table of n, a(n) for n=1..85.

Formula

a(1) = 0; for n > 1, a(n) = A347870(n) + a(n-1).

For all n >= 1, a(A347877(n)) = n.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342925(n) = A003415(sigma(n));
A347870(n) = (A342925(n)%2);
A349909(n) = if(1==n, A347870(n), A347870(n)+A349909(n-1));

Crossrefs

Cf. A000203, A003415, A342925, A347870, A347877, A349909.

Sequence in context: A337634 A316355 A055768 * A064952 A255070 A176001

Adjacent sequences: A349906 A349907 A349908 * A349910 A349911 A349912

Keyword

nonn

Author

Antti Karttunen, Feb 13 2022

Status

approved