A286258 Compound filter: a(n) = P(A046523(n), A046523(2n+1)), where P(n,k) is sequence A000027 used as a pairing function.

2, 5, 5, 25, 5, 27, 23, 44, 14, 61, 5, 117, 38, 27, 27, 226, 23, 90, 23, 90, 27, 142, 5, 375, 40, 27, 86, 148, 5, 495, 80, 698, 27, 61, 27, 702, 80, 61, 27, 765, 5, 625, 23, 90, 148, 61, 23, 1224, 109, 90, 27, 832, 5, 324, 61, 324, 61, 142, 23, 2013, 23, 84, 90, 2410, 27, 625, 302, 90, 27, 625, 23, 2998, 80, 27, 90, 265, 61, 495, 23, 1426, 152, 601, 5, 2013, 142, 27, 142

Offset

1,1

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

Prog

(PARI)
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
A286258(n) = (1/2)*(2 + ((A046523(n)+A046523((2*n)+1))^2) - A046523(n) - 3*A046523((2*n)+1));
for(n=1, 10000, write("b286258.txt", n, " ", A286258(n)));
(Scheme) (define (A286258 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A046523 (+ 1 n n))) 2) (- (A046523 n)) (- (* 3 (A046523 (+ 1 n n)))) 2)))
(Python)
from sympy import 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 a(n): return T(a046523(n), a046523(2*n + 1)) # Indranil Ghosh, May 07 2017

Crossrefs

Cf. A000027, A046523, A286255, A286256, A286257.

Cf. A005384 (gives the positions of 5's), A234095 (of 23's).

Sequence in context: A338586 A143818 A238879 * A297446 A154918 A176862

Adjacent sequences: A286255 A286256 A286257 * A286259 A286260 A286261

Keyword

nonn

Author

Antti Karttunen, May 07 2017

Status

approved