A069811 a(n) = Sum_{k=1..n} omega(k)^2.

0, 1, 2, 3, 4, 8, 9, 10, 11, 15, 16, 20, 21, 25, 29, 30, 31, 35, 36, 40, 44, 48, 49, 53, 54, 58, 59, 63, 64, 73, 74, 75, 79, 83, 87, 91, 92, 96, 100, 104, 105, 114, 115, 119, 123, 127, 128, 132, 133, 137, 141, 145, 146, 150, 154, 158, 162, 166, 167, 176, 177, 181

Offset

1,3

References

G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Fifth edition, Oxford University Press, Chap. XXII, p. 357.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Paul Turán, On a theorem of Hardy and Ramanujan, Journal of the London Mathematical Society, Vol. s1-9, No. 4 (1934), pp. 274-276.

Formula

a(n) = Sum_{k=1..n} A001221(k)^2.

a(n) = n*log(log(n))^2 + O(n*log(log(n))) (Turán, 1934).

a(n) = Sum_{k>=1} k^2 * A346617(n,k). - Alois P. Heinz, Aug 19 2021

Mathematica

Accumulate@((PrimeNu@Range@62)^2) (* Ivan Neretin, Mar 16 2017 *)

Prog

(PARI) a(n) = sum(k=1, n, omega(k)^2); \\ Michel Marcus, Mar 16 2017

Crossrefs

Equals (A074787(n)-1)/4 for n <= 29.

Cf. A001221, A346617.

Sequence in context: A061887 A005455 A047338 * A004826 A326783 A326785

Adjacent sequences: A069808 A069809 A069810 * A069812 A069813 A069814

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 30 2002

Status

approved