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

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

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

Prog

(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));

Crossrefs

Cf. also A085731, A322361, A347965, A348937.

Sequence in context: A111740 A327921 A155059 * A348498 A206076 A329374

Adjacent sequences: A347961 A347962 A347963 * A347965 A347966 A347967

Keyword

nonn

Author

Antti Karttunen, Sep 25 2021

Status

approved