OFFSET
1,4
COMMENTS
The original name was: Partial sums of A161840.
FORMULA
a(n) = Sum_{k=1..n} (tau(k)-2 + (tau(k) mod 2)), tau = A000005.
a(n) ~ n * (log(n) + 2*gamma - 3), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 19 2024
MAPLE
with(numtheory):
b:= n-> (x-> x-2+(x mod 2))(tau(n)):
a:= proc(n) option remember; b(n) +`if`(n=1, 0, a(n-1)) end:
seq(a(n), n=1..100);
MATHEMATICA
Accumulate[Table[d = DivisorSigma[0, n]; If[OddQ[d], d - 1, d - 2], {n, 100}]]
PROG
(PARI) lista(nmax) = {my(s = 0, d); for(n = 1, nmax, d = numdiv(n); s += (d + d%2 - 2); print1(s, ", ")); } \\ Amiram Eldar, Jan 19 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Jan 27 2011
EXTENSIONS
New name from Omar E. Pol, Jan 04 2022
STATUS
approved