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 A286164 Compound filter: a(n) = T(A055396(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function. 14
 0, 2, 5, 7, 9, 16, 14, 29, 12, 16, 20, 67, 27, 16, 23, 121, 35, 67, 44, 67, 23, 16, 54, 277, 18, 16, 38, 67, 65, 436, 77, 497, 23, 16, 31, 631, 90, 16, 23, 277, 104, 436, 119, 67, 80, 16, 135, 1129, 25, 67, 23, 67, 152, 277, 31, 277, 23, 16, 170, 1771, 189, 16, 80, 2017, 31, 436, 209, 67, 23, 436, 230, 2557, 252, 16, 80, 67, 40, 436, 275, 1129, 138, 16, 299 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 MathWorld, Pairing Function FORMULA a(n) = (1/2)*(2 + ((A055396(n)+A046523(n))^2) - A055396(n) - 3*A046523(n)). PROG (PARI) A001511(n) = (1+valuation(n, 2)); 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 A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])); \\ This function from Charles R Greathouse IV, Apr 23 2015 A286164(n) = (2 + ((A055396(n)+A046523(n))^2) - A055396(n) - 3*A046523(n))/2; for(n=1, 10000, write("b286164.txt", n, " ", A286164(n))); (Scheme) (define (A286164 n) (* (/ 1 2) (+ (expt (+ (A055396 n) (A046523 n)) 2) (- (A055396 n)) (- (* 3 (A046523 n))) 2))) (Python) from sympy import primepi, isprime, primefactors, factorint def a049084(n): return primepi(n)*(1*isprime(n)) def a055396(n): return 0 if n==1 else a049084(min(primefactors(n))) 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(a055396(n), a046523(n)) # Indranil Ghosh, May 05 2017 CROSSREFS Cf. A000027, A046523, A055396, A286160, A286161, A286162, A286163. Sequence in context: A253275 A093417 A286162 * A211167 A083272 A115906 Adjacent sequences:  A286161 A286162 A286163 * A286165 A286166 A286167 KEYWORD nonn AUTHOR Antti Karttunen, May 04 2017 STATUS approved

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)