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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Pairing Function

Formula

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

Prog

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

Crossrefs

Cf. A000027, A009191, A009194, A286594.

Sequence in context: A135021 A347811 A320412 * A297557 A066827 A016467

Adjacent sequences: A286588 A286589 A286590 * A286592 A286593 A286594

Keyword

nonn

Author

Antti Karttunen, May 21 2017

Status

approved