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
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
Programs
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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));
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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 -
Scheme
(define (A286571 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A017666 n)) 2) (- (A046523 n)) (- (* 3 (A017666 n))) 2)))