A286591 Compound filter: a(n) = P(A009191(n), A009194(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 3, 1, 1, 1, 23, 1, 10, 6, 5, 1, 42, 1, 5, 4, 1, 1, 34, 1, 5, 1, 5, 1, 179, 1, 5, 1, 408, 1, 23, 1, 3, 4, 5, 1, 45, 1, 5, 1, 144, 1, 23, 1, 12, 13, 5, 1, 12, 1, 3, 4, 5, 1, 23, 1, 113, 1, 5, 1, 265, 1, 5, 6, 1, 1, 23, 1, 5, 4, 5, 1, 103, 1, 5, 6, 12, 1, 23, 1, 65, 1, 5, 1, 753, 1, 5, 4, 63, 1, 259, 22, 12, 1, 5, 11, 265, 1, 3, 13, 1, 1, 23, 1, 44, 4, 5, 1

Offset: 1

Author

Antti Karttunen, May 21 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pairing Function

Crossrefs

Cf. A000027, A009191, A009194, A286594.

Programs

PARI

A009191(n) = gcd(n, numdiv(n));
A009194(n) = gcd(n, sigma(n));
A286591(n) = (1/2)*(2 + ((A009191(n)+A009194(n))^2) - A009191(n) - 3*A009194(n));

Python

from sympy import divisor_sigma, divisor_count, gcd
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a(n): return T(gcd(n, divisor_count(n)), gcd(n, divisor_sigma(n))) # Indranil Ghosh, May 22 2017

Scheme

(define (A286591 n) (* (/ 1 2) (+ (expt (+ (A009191 n) (A009194 n)) 2) (- (A009191 n)) (- (* 3 (A009194 n))) 2)))

Formula

a(n) = (1/2)*(2 + ((A009191(n)+A009194(n))^2) - A009191(n) - 3*A009194(n)).