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A349909 Partial sums of A347870; Number of terms of A347877 (numbers k with an odd arithmetic derivative of sigma(k)) in range 1..n. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)