A370131 a(n) = A068346(A276086(n)), where A068346 is the second arithmetic derivative, and A276086 is the primorial base exp-function.

0, 0, 0, 1, 5, 10, 0, 1, 12, 1, 16, 44, 7, 39, 16, 42, 608, 391, 55, 135, 365, 455, 1120, 2990, 800, 1100, 1400, 5425, 12575, 21025, 0, 6, 7, 1, 20, 103, 16, 1, 1, 32, 271, 320, 24, 78, 572, 459, 1031, 2887, 635, 1670, 1155, 3335, 19540, 22130, 4225, 7700, 18675, 28100, 68900, 155425, 9, 18, 20, 54, 704, 631, 24, 251

Offset

0,5

Links

Antti Karttunen, Table of n, a(n) for n = 0..2559

Index entries for sequences related to primorial base

Formula

a(n) = A068346(A276086(n)) = A003415(A327860(n)).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A370131(n) = A003415(A327860(n));

Crossrefs

Cf. A003415, A068346, A276086, A327860, A370130.

Cf. A002110 (positions of 0's after the initial zero), A328233 (positions of 1's), A328240 (positions of primes), A369651 (= a(A143293(n-1)), for n >= 1).

Sequence in context: A098135 A112259 A357280 * A258150 A330599 A099731

Adjacent sequences: A370128 A370129 A370130 * A370132 A370133 A370134

Keyword

nonn

Author

Antti Karttunen, Feb 10 2024

Status

approved