A373842 a(n) = A003415(A276085(n)), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

0, 0, 1, 1, 5, 1, 31, 1, 4, 1, 247, 4, 2927, 1, 12, 4, 40361, 1, 716167, 12, 80, 1, 14117683, 1, 16, 1, 5, 80, 334406399, 6, 9920878441, 1, 216, 568, 60, 5, 314016924901, 33975, 3740, 6, 11819186711467, 14, 492007393304957, 216, 7, 28300, 21460568175640361, 5, 92, 1, 60080, 3740, 1021729465586766997, 1, 540, 14

Offset: 1

Author

Antti Karttunen, Jun 20 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..481

Crossrefs

Cf. A003415, A024451, A276085, A373843 [= gcd(n, a(n))], A373846 (positions of 1's), A373847 [k such that a(n)<=k], A373848.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
A373842(n) = A003415(A276085(n));

Formula

For n >= 1, a(A000040(n)) = A024451(n-1).