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

Author

Gary W. Adamson, Aug 03 2008

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A143271, A000005, A000217.

Programs

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 *)

PARI

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

Formula

Equals row sums of triangle A143271

Extensions

Extended by Emeric Deutsch, Aug 16 2008