A353573 Greatest common divisor of A342002 and its shifted variant, where A342002(n) = A003415(A276086(n)) / A003557(A276086(n)) and A276086 is the primorial base exp-function.

0, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 8, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1

Offset: 0

Author

Antti Karttunen, Apr 29 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A003557, A003961, A342001, A342002, A353572, A353574.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A342001(n) = (A003415(n) / A003557(n));
A353571(n) = A342001(A003961(n));
A353573(n) = gcd(A353571(A276086(n)), A342001(A276086(n)));

Formula

a(n) = gcd(A342002(n), A353572(n)).

a(n) = gcd(A353571(A276086(n)), A342001(A276086(n))).

For all n >= 1, a(n) = A342002(n) / A353574(n).