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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. 5
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:

        if P(n) == P(x): return x

        else: x+=1

def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

def a(n): return T(a051064(n), a046523(n)) # Indranil Ghosh, May 11 2017

CROSSREFS

Cf. A000027, A046523, A051064, A286161, A286461, A286462, A286464.

Sequence in context: A095795 A088531 A291756 * A286362 A309200 A097964

Adjacent sequences:  A286460 A286461 A286462 * A286464 A286465 A286466

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 10 2017

STATUS

approved

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Last modified May 15 01:43 EDT 2021. Contains 343909 sequences. (Running on oeis4.)