OFFSET
1,11
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..2500
FORMULA
Moebius transform is the period 288 sequence A257477.
a(3*n) = a(4*n) = a(8*n + 5) = a(8*n + 7) = 0. a(2*n + 1) = a(4*n + 2).
a(24*n + 1) = A257398(n). a(24*n + 11) = 2*A255318(n). a(24*n + 17) = 2*A255319(n). a(24*n + 19) = 2*A255317(n).
From Michael Somos, Apr 22 2015: (Start)
Expansion of F(q) + F(q^2) + G(q) + G(q^2) in powers of q where F(q) = q * A257399(q^6) and G(q) = 2 * q^11 * A257402(q^6). (End)
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi/(6*sqrt(2)) = 0.370240... . - Amiram Eldar, Oct 17 2022
EXAMPLE
G.f. = x + x^2 + 2*x^11 + 2*x^17 + 2*x^19 + 2*x^22 + x^25 + 2*x^34 + ...
MATHEMATICA
a[ n_] := If[ n < 2, Boole[n == 1], Times @@ (Which[ # == 2, Boole[#2 == 1], # == 3, 0, Mod[#, 8] < 4, #2 + 1, True, Mod[#2 + 1, 2]]& @@@ FactorInteger[n])];
PROG
(PARI) {a(n) = my(A, p, e); if( n<1, 0, A = factor(n); prod( k=1, matsize(A)[1], [p, e] = A[k, ]; if( p<5, p+e==3, p%8 > 4, 1-e%2, e+1)))};
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Michael Somos, Apr 21 2015
STATUS
approved