A390442 a(n) = Sum_{k<=10^n} d(k^2), where d(k^2) = number of divisors function A000005 for k^2.

1, 48, 1194, 22502, 363982, 5351260, 73858790, 974287906, 12422233000, 154239024036, 1874789312770, 22394201768192, 263628273676370, 3065376975230230, 35267028900050368, 402026048037526536, 4546049746278221498, 51040706877167591310, 569432330468205745412

Offset

0,2

Links

Henri Lifchitz, Table of n, a(n) for n = 0..20

Formula

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

a(n) = A061503(10^n).

Example

a(1) = d(1^2) + d(2^2) + d(3^2) +...+ d(8^2) + d(9^2) + d(10^2) = 48

Mathematica

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

Prog

(PARI) a(n) = sum(k=1, 10^n, numdiv(k^2)); \\ Michel Marcus, Nov 06 2025

Crossrefs

Cf. A000005, A061503, A057494.

Sequence in context: A369561 A011000 A025233 * A004425 A082558 A285169

Adjacent sequences: A390439 A390440 A390441 * A390443 A390444 A390445

Keyword

nonn

Author

Henri Lifchitz, Nov 05 2025

Status

approved