OFFSET
1,6
COMMENTS
For n >= 2, a(n) is the number of partitions of n-1 into 3 parts such that the largest part is greater than or equal to the product of the other two. For example, a(9) = 4 since the partitions for 8 would be 1+1+6 = 1+2+5 = 1+3+4 = 2+2+4, but not 2+3+3 since 2*3 > 3. - Wesley Ivan Hurt, Jan 03 2022
Conjecture: partial sums of A072670. - Sean A. Irvine, Jul 14 2022
FORMULA
a(n) = Sum_{k=1..floor((n-1)/3)} Sum_{i=k..floor((n-k-1)/2)} sign(floor((n-i-k-1)/(i*k))). - Wesley Ivan Hurt, Jan 03 2022
a(n) = (1/2) * Sum_{k=1..n} (tau(k)-2 + (tau(k) mod 2)), tau = A000005. - Alois P. Heinz, Jan 04 2022
a(n) ~ n * (log(n) + 2*gamma - 3) / 2, where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 19 2024
MATHEMATICA
Accumulate[Table[d = DivisorSigma[0, n]; If[OddQ[d], d - 1, d - 2], {n, 100}]]/2
PROG
(PARI) a(n) = sum(k=1, n, numdiv(k) - 2 + numdiv(k)%2)/2; \\ Michel Marcus, Jan 04 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Jan 27 2011
STATUS
approved