A340071 a(n) = gcd(A003961(n)-1, phi(A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes.

1, 2, 4, 2, 6, 2, 10, 2, 4, 4, 12, 4, 16, 4, 2, 2, 18, 2, 22, 2, 2, 2, 28, 2, 6, 2, 4, 2, 30, 8, 36, 2, 16, 4, 4, 8, 40, 4, 4, 4, 42, 4, 46, 4, 6, 2, 52, 4, 10, 2, 2, 8, 58, 2, 18, 4, 2, 4, 60, 2, 66, 2, 2, 2, 2, 2, 70, 2, 16, 10, 72, 2, 78, 2, 4, 2, 2, 2, 82, 2, 4, 4, 88, 2, 12, 4, 2, 2, 96, 4, 2, 4, 8, 2, 4, 2, 100

Offset: 1

Author

Antti Karttunen, Dec 28 2020

Keywords

• nonn

Comments

Prime shifted analog of A049559.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000010, A003961, A003972, A049559, A253885, A340072, A340073.

Cf. also A340081.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A340071(n) = { my(u=A003961(n)); gcd(u-1, eulerphi(u)); };

Formula

a(n) = A049559(A003961(n)).

a(n) = gcd(A253885(n-1), A003972(n)) = gcd(A003961(n)-1, A000010(A003961(n))).

a(n) = A003972(n) / A340072(n).

For n > 1, a(n) = (A003961(n)-1) / A340073(n).