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 A286163 Compound filter: a(n) = T(A046523(n), A278222(n)), where T(n,k) is sequence A000027 used as a pairing function. 16
 2, 5, 12, 14, 23, 42, 38, 44, 40, 61, 80, 117, 80, 84, 216, 152, 23, 148, 80, 148, 601, 142, 302, 375, 109, 142, 911, 183, 302, 1020, 530, 560, 61, 61, 142, 856, 467, 142, 412, 430, 467, 1741, 1832, 265, 2497, 412, 1178, 1323, 109, 265, 826, 265, 1832, 1735, 2932, 489, 412, 412, 2630, 2835, 1178, 672, 2787, 2144, 61, 625, 80, 148, 601, 850, 302, 2998, 467, 601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 MathWorld, Pairing Function FORMULA a(n) = (1/2)*(2 + ((A046523(n)+A278222(n))^2) - A046523(n) - 3*A278222(n)). PROG (PARI) A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler 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 A278222(n) = A046523(A005940(1+n)); A286163(n) = (2 + ((A046523(n)+A278222(n))^2) - A046523(n) - 3*A278222(n))/2; for(n=1, 10000, write("b286163.txt", n, " ", A286163(n))); (Scheme) (define (A286163 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A278222 n)) 2) (- (A046523 n)) (- (* 3 (A278222 n))) 2))) (Python) from sympy import prime, factorint import math def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2 def A(n): return n - 2**int(math.floor(math.log(n, 2))) def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n)) def a005940(n): return b(n - 1) 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 a278222(n): return a046523(a005940(n + 1)) def a(n): return T(a046523(n), a278222(n)) # Indranil Ghosh, May 05 2017 CROSSREFS Cf. A000027, A046523, A278222, A286160, A286161, A286162, A286164. Sequence in context: A114217 A286255 A286160 * A286240 A215974 A192524 Adjacent sequences:  A286160 A286161 A286162 * A286164 A286165 A286166 KEYWORD nonn AUTHOR Antti Karttunen, May 04 2017 STATUS approved

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Last modified June 18 06:02 EDT 2021. Contains 345098 sequences. (Running on oeis4.)