A143272 a(n) = d(n)*T(n), where d(n) is the number of divisors of n (A000005) and T(n)=n(n+1)/2 are the triangular numbers (A000217).

1, 6, 12, 30, 30, 84, 56, 144, 135, 220, 132, 468, 182, 420, 480, 680, 306, 1026, 380, 1260, 924, 1012, 552, 2400, 975, 1404, 1512, 2436, 870, 3720, 992, 3168, 2244, 2380, 2520, 5994, 1406, 2964, 3120, 6560, 1722, 7224, 1892, 5940, 6210, 4324, 2256, 11760

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Equals row sums of triangle A143271

Example

a(4) = 30 = d(4)*T(4) = 3*10, where A000005 = (1, 2, 2, 3, 2, 4, ...) and A000217 = (1, 3, 6, 10, ...).

Maple

with(numtheory): seq((1/2)*tau(n)*n*(n+1), n=1..50); # Emeric Deutsch, Aug 16 2008

Mathematica

Table[DivisorSigma[0, n] (n(n+1))/2, {n, 50}] (* Harvey P. Dale, Sep 05 2017 *)

Prog

(PARI) a(n) = numdiv(n)*n*(n+1)/2; \\ Michel Marcus, Mar 11 2019

Crossrefs

Cf. A143271, A000005, A000217.

Sequence in context: A124679 A242949 A341637 * A153877 A229491 A263676

Adjacent sequences: A143269 A143270 A143271 * A143273 A143274 A143275

Keyword

nonn

Author

Gary W. Adamson, Aug 03 2008

Extensions

Extended by Emeric Deutsch, Aug 16 2008

Status

approved