A286452 Compound filter (largest prime factor of n & prime signature of 2n-1): a(n) = P(A061395(n), A046523(2n-1)), where P(n,k) is sequence A000027 used as a pairing function.
0, 2, 5, 2, 18, 5, 14, 16, 5, 9, 50, 5, 42, 59, 9, 2, 73, 23, 44, 31, 14, 20, 199, 5, 18, 61, 5, 40, 115, 9, 77, 67, 50, 35, 40, 5, 90, 179, 61, 9, 391, 14, 185, 50, 9, 100, 205, 23, 14, 94, 35, 27, 1006, 5, 20, 40, 44, 115, 395, 31, 228, 131, 59, 2, 61, 20, 295, 442, 54, 14, 320, 23, 346, 265, 9, 44, 125, 61, 275, 31, 23, 104, 1349, 14, 52, 314, 65, 125, 430
Offset: 1
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
- Eric Weisstein's World of Mathematics, Pairing Function
Programs
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Python
from sympy import primepi, primefactors, 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 a061395(n): return 0 if n==1 else primepi(primefactors(n)[-1]) def a(n): return T(a061395(n), a046523(2*n - 1)) # Indranil Ghosh, May 14 2017 -
Scheme
(define (A286452 n) (* (/ 1 2) (+ (expt (+ (A061395 n) (A046523 (+ n n -1))) 2) (- (A061395 n)) (- (* 3 (A046523 (+ n n -1)))) 2)))