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A286591
Compound filter: a(n) = P(A009191(n), A009194(n)), where P(n,k) is sequence A000027 used as a pairing function.
4
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 21 2017
STATUS
approved