A347964 Greatest common divisor of A003415 (arithmetic derivative) and A003961 (prime shift towards larger primes).

1, 1, 1, 1, 1, 5, 1, 3, 1, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 5, 13, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 19, 1, 15, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 5, 1, 1, 3, 1, 1, 1, 31, 1, 1, 1, 3, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 3, 5, 1, 1, 1, 1, 1, 1, 43, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 11, 25, 7

Offset: 1

Author

Antti Karttunen, Sep 25 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. also A085731, A322361, A347965, A348937.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A347964(n) = gcd(A003415(n), A003961(n));

Formula

a(n) = gcd(A003415(n), A003961(n)).

a(n) = gcd(A003415(n), A348937(n)) = gcd(A003961(n), A348937(n)). - Antti Karttunen, Dec 06 2021