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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

%I

%S 1,6,12,30,30,84,56,144,135,220,132,468,182,420,480,680,306,1026,380,

%T 1260,924,1012,552,2400,975,1404,1512,2436,870,3720,992,3168,2244,

%U 2380,2520,5994,1406,2964,3120,6560,1722,7224,1892,5940,6210,4324,2256,11760

%N 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).

%H Harvey P. Dale, <a href="/A143272/b143272.txt">Table of n, a(n) for n = 1..1000</a>

%F Equals row sums of triangle A143271

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

%p with(numtheory): seq((1/2)*tau(n)*n*(n+1),n=1..50); # _Emeric Deutsch_, Aug 16 2008

%t Table[DivisorSigma[0,n] (n(n+1))/2,{n,50}] (* _Harvey P. Dale_, Sep 05 2017 *)

%o (PARI) a(n) = numdiv(n)*n*(n+1)/2; \\ _Michel Marcus_, Mar 11 2019

%Y Cf. A143271, A000005, A000217.

%K nonn

%O 1,2

%A _Gary W. Adamson_, Aug 03 2008

%E Extended by _Emeric Deutsch_, Aug 16 2008

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Last modified January 21 19:33 EST 2021. Contains 340352 sequences. (Running on oeis4.)