A286356 Compound filter: a(n) = P(A061395(n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function.

0, 2, 5, 7, 9, 23, 14, 29, 12, 31, 20, 80, 27, 40, 31, 121, 35, 80, 44, 94, 40, 50, 54, 302, 18, 61, 38, 109, 65, 499, 77, 497, 50, 73, 40, 668, 90, 86, 61, 328, 104, 532, 119, 125, 94, 100, 135, 1178, 25, 94, 73, 142, 152, 302, 50, 355, 86, 115, 170, 1894, 189, 131, 109, 2017, 61, 566, 209, 160, 100, 532, 230, 2630, 252, 148, 94, 179, 50, 601, 275, 1228, 138

Offset: 1

Author

Antti Karttunen, May 09 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pairing Function

Crossrefs

Cf. A000027, A046523, A061395, A286164.

Programs

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
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After M. F. Hasler's code for A006530.
A286356(n) = (2 + ((A061395(n)+A046523(n))^2) - A061395(n) - 3*A046523(n))/2;
for(n=1, 10000, write("b286356.txt", n, " ", A286356(n)));

Python

from sympy import factorint
from operator import mul
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(max(primefactors(n)))
def a(n): return T(a061395(n), a046523(n)) # Indranil Ghosh, May 09 2017

Scheme

(define (A286356 n) (* (/ 1 2) (+ (expt (+ (A061395 n) (A046523 n)) 2) (- (A061395 n)) (- (* 3 (A046523 n))) 2)))

Formula

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