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A286253
Compound filter: a(n) = P(A055396(n), A001511(1+n)), where P(n,k) is sequence A000027 used as a pairing function.
4
0, 1, 8, 1, 9, 1, 25, 1, 5, 1, 26, 1, 27, 1, 17, 1, 35, 1, 53, 1, 5, 1, 75, 1, 9, 1, 8, 1, 65, 1, 131, 1, 5, 1, 13, 1, 90, 1, 12, 1, 104, 1, 134, 1, 5, 1, 186, 1, 14, 1, 8, 1, 152, 1, 18, 1, 5, 1, 188, 1, 189, 1, 30, 1, 9, 1, 229, 1, 5, 1, 273, 1, 252, 1, 8, 1, 14, 1, 347, 1, 5, 1, 323, 1, 9, 1, 12, 1, 324, 1, 19, 1, 5, 1, 31, 1, 350, 1, 8, 1, 377, 1, 462, 1, 5
OFFSET
1,3
LINKS
FORMULA
a(n) = (1/2)*(2 + ((A055396(n)+A001511(1+n))^2) - A055396(n) - 3*A001511(1+n)).
PROG
(PARI)
A001511(n) = (1+valuation(n, 2));
A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])); \\ This function from Charles R Greathouse IV, Apr 23 2015
A286253(n) = (2 + ((A055396(n)+A001511(1+n))^2) - A055396(n) - 3*A001511(1+n))/2;
for(n=1, 10000, write("b286253.txt", n, " ", A286253(n)));
(Scheme) (define (A286253 n) (* (/ 1 2) (+ (expt (+ (A055396 n) (A001511 (+ 1 n))) 2) (- (A055396 n)) (- (* 3 (A001511 (+ 1 n)))) 2)))
(Python)
from sympy import primepi, isprime, primefactors
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a049084(n): return primepi(n)*(1*isprime(n))
def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")
def a(n): return T(a055396(n), a001511(n + 1)) # Indranil Ghosh, May 07 2017
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 07 2017
STATUS
approved