A141677 Number of divisors of n times the number of primes <= n.

0, 2, 4, 6, 6, 12, 8, 16, 12, 16, 10, 30, 12, 24, 24, 30, 14, 42, 16, 48, 32, 32, 18, 72, 27, 36, 36, 54, 20, 80, 22, 66, 44, 44, 44, 99, 24, 48, 48, 96, 26, 104, 28, 84, 84, 56, 30, 150, 45, 90, 60, 90, 32, 128, 64, 128, 64, 64, 34, 204, 36, 72, 108, 126, 72, 144, 38, 114, 76

Offset

1,2

Comments

Only five in the first 200 indices give odd values: 25, 36, 49, 100, 169.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

a(n) = A000005(n)*A000720(n).

Example

For n=12, the number of divisors is 6 (1, 2, 3, 4, 6, and 12), and the number of primes <= n is 5 (2, 3, 5, 7, and 11).  So a(12) = 6 * 5 = 30. - Michael B. Porter, Jun 08 2018

Mathematica

Table[DivisorSigma[0, n]*PrimePi[n], {n, 1, 100}]

Prog

(PARI) for(n=1, 100, print1(numdiv(n)*primepi(n), ", ")) \\ G. C. Greubel, Jun 05 2018

Crossrefs

Cf. A000005, A000720.

Sequence in context: A359671 A222733 A364828 * A087459 A285103 A123258

Adjacent sequences: A141674 A141675 A141676 * A141678 A141679 A141680

Keyword

nonn

Author

Roger L. Bagula, Sep 07 2008

Extensions

Edited by the Associate Editors of the OEIS, Jun 08 2018

Status

approved