OFFSET
1,3
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
FORMULA
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 - (p - q(p))/p^2) = 0.526221951..., where q(2) = 1, and q(p) = A151799(p) for an odd prime p. - Amiram Eldar, Nov 02 2023
EXAMPLE
a(63) = a(3^2*7^1) = a(3^2)*a(7^1) = (2*3^1)*(5*7^0) = 30.
MATHEMATICA
f[p_, e_] := If[p == 2, 1, NextPrime[p, -1]]*p^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 02 2023 *)
PROG
(PARI)
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0, f[i, 2]-1)); factorback(f); };
A065769(n) = { my(f=factor(n>>valuation(n, 2))[, 1]~); (A003557(n) * factorback(vector(#f, i, precprime(f[i]-1)))); }; \\ Antti Karttunen, Dec 31 2017
CROSSREFS
KEYWORD
mult,nonn,easy
AUTHOR
Henry Bottomley, Nov 19 2001
STATUS
approved