A286463 - OEIS

A286463

Compound filter (3-adic valuation & prime-signature): a(n) = P(A051064(n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 2, 5, 7, 2, 23, 2, 29, 18, 16, 2, 80, 2, 16, 23, 121, 2, 94, 2, 67, 23, 16, 2, 302, 7, 16, 59, 67, 2, 467, 2, 497, 23, 16, 16, 706, 2, 16, 23, 277, 2, 467, 2, 67, 94, 16, 2, 1178, 7, 67, 23, 67, 2, 355, 16, 277, 23, 16, 2, 1832, 2, 16, 94, 2017, 16, 467, 2, 67, 23, 436, 2, 2704, 2, 16, 80, 67, 16, 467, 2, 1129, 195, 16, 2, 1832, 16, 16, 23, 277, 2, 1894, 16

(list; graph; refs; listen; history; text; internal format)

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 + ((A051064(n)+A046523(n))^2) - A051064(n) - 3*A046523(n)).

PROG

(PARI)

A051064(n) = if(n<1, 0, 1+valuation(n, 3));

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from Charles R Greathouse IV, Aug 17 2011

A286463(n) = (1/2)*(2 + ((A051064(n)+A046523(n))^2) - A051064(n) - 3*A046523(n));

for(n=1, 10000, write("b286463.txt", n, " ", A286463(n)));

(Scheme) (define (A286463 n) (* (/ 1 2) (+ (expt (+ (A051064 n) (A046523 n)) 2) (- (A051064 n)) (- (* 3 (A046523 n))) 2)))

(Python)

from sympy import factorint, divisors, divisor_count, mobius

def a051064(n): return -sum([mobius(3*d)*divisor_count(n/d) for d in divisors(n)])

def P(n):

f = factorint(n)

return sorted([f[i] for i in f])

def a046523(n):

x=1

while True: