A351083 a(n) = gcd(n, A003415(A276086(n))), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

0, 1, 1, 1, 2, 1, 1, 7, 8, 1, 1, 1, 2, 1, 1, 5, 16, 1, 3, 1, 10, 1, 1, 1, 4, 25, 1, 1, 2, 1, 1, 1, 2, 1, 17, 5, 12, 1, 1, 13, 2, 1, 1, 1, 4, 5, 1, 1, 2, 1, 25, 1, 4, 1, 3, 5, 2, 1, 1, 1, 2, 1, 1, 7, 4, 1, 1, 1, 2, 1, 7, 1, 24, 1, 1, 5, 2, 7, 1, 1, 80, 1, 1, 1, 14, 5, 1, 1, 8, 1, 3, 91, 4, 1, 1, 1, 2, 1, 49, 1, 4

Offset: 0

Author

Antti Karttunen, Feb 03 2022

Keywords

• nonn
• base
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A324198, A327860, A328572, A351080, A351084, A351087 (fixed points), A354823 (Dirichlet inverse), A373145, A373599 (indices of multiples of 3 in this sequence).

Cf. A166486 (a(n) mod 2, parity of terms, see comment in A327860).

Cf. also A345000.

Programs

Mathematica

Array[Block[{i, m, n = #, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; GCD[#, If[m < 2, 0, m Total[#2/#1 & @@@ FactorInteger[m]]]]] &, 101, 0] (* Michael De Vlieger, Feb 04 2022 *)

PARI

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); };
A351083(n) = gcd(n, A327860(n));

Formula

a(n) = gcd(n, A327860(n)) = gcd(n, A003415(A276086(n))).

a(n) = A373145(A276086(n)). - Antti Karttunen, Jun 18 2024