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