A340073 a(n) = (x-1) / gcd(x-1, phi(x)), where x = A003961(n), i.e., n with its prime factorization shifted one step towards larger primes.

0, 1, 1, 4, 1, 7, 1, 13, 6, 5, 1, 11, 1, 8, 17, 40, 1, 37, 1, 31, 27, 19, 1, 67, 8, 25, 31, 49, 1, 13, 1, 121, 4, 14, 19, 28, 1, 17, 21, 47, 1, 41, 1, 29, 29, 43, 1, 101, 12, 73, 47, 19, 1, 187, 5, 74, 57, 23, 1, 157, 1, 55, 137, 364, 59, 97, 1, 85, 9, 23, 1, 337, 1, 61, 61, 103, 71, 127, 1, 283, 156, 32, 1, 247, 11

Offset: 1

Author

Antti Karttunen, Dec 28 2020

Keywords

• nonn

Comments

Prime shifted analog of A160596.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000010, A003961, A003972, A160596, A253885, A340071, A340072.

Cf. also A340083.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A340073(n) = { my(x=A003961(n)); (x-1)/gcd(x-1, eulerphi(x)); };

Formula

a(n) = A160596(A003961(n)).

a(n) = A253885(n-1) / A340071(n) = (A003961(n)-1) / A340071(n).