A386602 a(n) = Sum_{k<=10^n} d(k)^2, where d(k) = number of divisors function A000005.

1, 83, 3046, 75083, 1504136, 26324772, 421094344, 6313765566, 90150976452, 1238908414238, 16509952757456, 214519154750835, 2728918556059128, 34095978349861305, 419465099018376120, 5091499634810776756, 61075653860888936424, 725026986157444779126

Offset

0,2

Links

Henri Lifchitz, Table of n, a(n) for n = 0..19

Formula

a(n) = Sum_{k=1..10^n} d(k)^2.

a(n) = Sum_{i=1..floor(sqrt(10^n))} mu(i)*A061202(floor(10^n/i^2)).

Example

The first numbers of divisors are: 1,2,2,3,2,4,2,4,3,4, ... (A000005)
So, a(1) = 1 + 4*(2^2) + 2*(3^2) + 3*(4^2) = 83.

Mathematica

Table[Sum[DivisorSigma[0, k]^2, {k, 1, 10^n}], {n, 0, 5}]

Crossrefs

Cf. A000005, A061202, A061502.

Sequence in context: A332615 A156924 A084299 * A017799 A017746 A220649

Adjacent sequences: A386599 A386600 A386601 * A386603 A386604 A386605

Keyword

nonn

Author

Henri Lifchitz, Oct 22 2025

Status

approved