A286571 Compound filter (prime signature of n & n/gcd(n, sigma(n))): a(n) = P(A046523(n), A017666(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 5, 8, 25, 17, 21, 30, 113, 70, 51, 68, 103, 93, 72, 51, 481, 155, 148, 192, 222, 331, 126, 278, 324, 382, 159, 569, 78, 437, 591, 498, 1985, 126, 237, 786, 2521, 705, 282, 952, 375, 863, 660, 948, 243, 337, 384, 1130, 1759, 1330, 1842, 237, 678, 1433, 520, 1776, 459, 1897, 567, 1772, 2076, 1893, 636, 2713, 8065, 2421, 810, 2280, 1002, 384, 2046

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = (1/2)*(2 + ((A046523(n)+A017666(n))^2) - A046523(n) - 3*A017666(n)).

Prog

(PARI)
A017666(n) = (n/gcd(n, sigma(n)));
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
A286571(n) = (1/2)*(2 + ((A046523(n)+A017666(n))^2) - A046523(n) - 3*A017666(n));
(Scheme) (define (A286571 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A017666 n)) 2) (- (A046523 n)) (- (* 3 (A017666 n))) 2)))
(Python)
from sympy import factorint, gcd, divisor_sigma
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), n/gcd(n, divisor_sigma(n))) # Indranil Ghosh, May 26 2017

Crossrefs

Cf. A000027, A017666, A046523, A286360, A286570.

Sequence in context: A346552 A375350 A166652 * A234334 A025623 A069959

Adjacent sequences: A286568 A286569 A286570 * A286572 A286573 A286574

Keyword

nonn

Author

Antti Karttunen, May 26 2017

Status

approved