A340149 Odd part of A340147: a(n) = A000265(A247074(A003961(n))).

1, 1, 1, 3, 1, 1, 1, 9, 5, 3, 1, 3, 1, 5, 3, 27, 1, 5, 1, 9, 5, 3, 1, 9, 7, 1, 25, 15, 1, 3, 1, 81, 3, 9, 15, 15, 1, 11, 1, 27, 1, 5, 1, 9, 5, 7, 1, 27, 11, 21, 9, 3, 1, 25, 1, 45, 11, 15, 1, 9, 1, 9, 25, 243, 3, 3, 1, 27, 7, 3, 1, 45, 1, 5, 21, 33, 15, 1, 1, 81, 125, 21, 1, 15, 3, 23, 15, 27, 1, 15, 5, 21, 9, 13, 33

Offset: 1

Author

Antti Karttunen, Dec 30 2020

Keywords

• nonn

Comments

Each term a(n) is a divisor of A340075(n), at n=85 occurs the first proper divisor.

Links

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

Crossrefs

Cf. A000265, A003961, A247074, A340147, A340150 (positions of ones).

Differs from related A340075 for the first time at n=85, where a(85) = 3, while A340075(85) = 9.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A247074(n) = { my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); }; \\ From A247074
A340149(n) = A000265(A247074(A003961(n)));

Formula

a(n) = A000265(A340147(n)) = A000265(A247074(A003961(n))).