A286452 Compound filter (largest prime factor of n & prime signature of 2n-1): a(n) = P(A061395(n), A046523(2n-1)), where P(n,k) is sequence A000027 used as a pairing function.

0, 2, 5, 2, 18, 5, 14, 16, 5, 9, 50, 5, 42, 59, 9, 2, 73, 23, 44, 31, 14, 20, 199, 5, 18, 61, 5, 40, 115, 9, 77, 67, 50, 35, 40, 5, 90, 179, 61, 9, 391, 14, 185, 50, 9, 100, 205, 23, 14, 94, 35, 27, 1006, 5, 20, 40, 44, 115, 395, 31, 228, 131, 59, 2, 61, 20, 295, 442, 54, 14, 320, 23, 346, 265, 9, 44, 125, 61, 275, 31, 23, 104, 1349, 14, 52, 314, 65, 125, 430

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 + ((A061395(n)+A046523(2n-1))^2) - A061395(n) - 3*A046523(2n-1)).

Prog

(Scheme) (define (A286452 n) (* (/ 1 2) (+ (expt (+ (A061395 n) (A046523 (+ n n -1))) 2) (- (A061395 n)) (- (* 3 (A046523 (+ n n -1)))) 2)))
(Python)
from sympy import primepi, primefactors, factorint
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
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 a061395(n): return 0 if n==1 else primepi(primefactors(n)[-1])
def a(n): return T(a061395(n), a046523(2*n - 1)) # Indranil Ghosh, May 14 2017

Crossrefs

Cf. A000027, A046523, A061395, A278223, A285334, A286356, A286372, A286453.

Sequence in context: A340043 A257514 A089120 * A298664 A319201 A019295

Adjacent sequences: A286449 A286450 A286451 * A286453 A286454 A286455

Keyword

nonn

Author

Antti Karttunen, May 14 2017

Status

approved