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 A286162 Compound filter: a(n) = T(A001511(n), A278222(n)), where T(n,k) is sequence A000027 used as a pairing function. 16
 2, 5, 7, 9, 16, 12, 29, 14, 16, 23, 67, 18, 67, 38, 121, 20, 16, 23, 67, 31, 436, 80, 277, 25, 67, 80, 631, 48, 277, 138, 497, 27, 16, 23, 67, 31, 436, 80, 277, 40, 436, 467, 1771, 94, 1771, 302, 1129, 33, 67, 80, 631, 94, 1771, 668, 2557, 59, 277, 302, 2557, 156, 1129, 530, 2017, 35, 16, 23, 67, 31, 436, 80, 277, 40, 436, 467, 1771, 94, 1771, 302, 1129, 50 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 + ((A001511(n)+A278222(n))^2) - A001511(n) - 3*A278222(n)). PROG (PARI) A001511(n) = (1+valuation(n, 2)); 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)); A286162(n) = (2 + ((A001511(n)+A278222(n))^2) - A001511(n) - 3*A278222(n))/2; for(n=1, 10000, write("b286162.txt", n, " ", A286162(n))); (Scheme) (define (A286162 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A278222 n)) 2) (- (A001511 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 a001511(n): return bin(n)[2:][::-1].index("1") + 1 def a(n): return T(a001511(n), a278222(n)) # Indranil Ghosh, May 05 2017 CROSSREFS Cf. A000027, A001511, A278222, A286160, A286161, A286163, A286164. Sequence in context: A287363 A253275 A093417 * A286164 A211167 A083272 Adjacent sequences:  A286159 A286160 A286161 * A286163 A286164 A286165 KEYWORD nonn AUTHOR Antti Karttunen, May 04 2017 STATUS approved

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Last modified June 20 13:10 EDT 2021. Contains 345164 sequences. (Running on oeis4.)