OFFSET
1,3
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1.
FORMULA
a(n) = Sum_{k=1..n} (-1)^(k+1) * A055231(k).
a(n) = (5/38) * c * n^2 + O(R(n)), where c = Product_{p prime} (1 - (p^2+p-1)/(p^3*(p+1))) = 0.649606... (A191622), R(n) = x^(3/2) * exp(-c_1 * log(n)^(3/5) / log(log(n))^(1/5)) unconditionally, or x^(7/5) * exp(c_2 * log(n) / log(log(n))) assuming the Riemann hypothesis, and c_1 and c_2 are positive constants (Tóth, 2017).
MATHEMATICA
f[p_, e_] := If[e == 1, p, 1]; pfp[n_] := Times @@ f @@@ FactorInteger[n]; pfp[1] = 1; Accumulate[Array[(-1)^(# + 1) * pfp[#] &, 100]]
PROG
(PARI) pfp(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1, f[i, 1], 1)); }
lista(kmax) = {my(s = 0); for(k = 1, kmax, s += (-1)^(k+1) * pfp(k); print1(s, ", "))};
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Amiram Eldar, Mar 05 2024
STATUS
approved