

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).


2



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
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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: A079390 A124679 A242949 * 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



