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

1,2

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

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

Crossrefs

Cf. A000027, A046523, A061395, A286164.

Sequence in context: A083272 A115906 A192279 * A086422 A046880 A142879

Adjacent sequences: A286353 A286354 A286355 * A286357 A286358 A286359

Keyword

nonn

Author

Antti Karttunen, May 09 2017

Status

approved