A342016 Difference between the arithmetic derivative of A276086(n) and A276086(n) itself, which is the prime product form of primorial base expansion of n.

-1, -1, -2, -1, -3, 3, -4, -3, -7, 1, -6, 33, -15, -5, -20, 35, 15, 255, -50, 25, -25, 325, 300, 1725, -125, 375, 250, 2375, 2625, 10875, -6, -5, -11, -1, -12, 39, -23, -11, -34, 37, 3, 321, -80, 15, -65, 395, 330, 2235, -225, 425, 200, 3025, 3225, 14325, -250, 3875, 3625, 20375, 24000, 87375, -35, -21, -56, 35, -21

Offset: 0

Author

Antti Karttunen, Mar 04 2021

Keywords

• sign
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2310
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A168036, A276086, A327860, A328572, A342002, A342015, A342026.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327860(n) = A003415(A276086(n));
A342016(n) = (A327860(n) - A276086(n));

Formula

a(n) = A168036(A276086(n)) = A327860(n) - A276086(n).

For all n >= 0, gcd(a(n), A276086(n)) = gcd(a(n), A327860(n)) = A328572(n).