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A060872 Sum of d*d' over all unordered pairs (d,d') with d*d' = n. 4

%I

%S 1,2,3,8,5,12,7,16,18,20,11,36,13,28,30,48,17,54,19,60,42,44,23,96,50,

%T 52,54,84,29,120,31,96,66,68,70,180,37,76,78,160,41,168,43,132,135,92,

%U 47,240,98,150,102,156,53,216,110,224,114,116,59,360,61,124,189,256

%N Sum of d*d' over all unordered pairs (d,d') with d*d' = n.

%H Vincenzo Librandi, <a href="/A060872/b060872.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = n * ceiling( d(n)/2) where d is the number of divisors function.

%F G.f.: x*f'(x), where f(x) = Sum_{k>=1} x^k^2/(1 - x^k). - _Ilya Gutkovskiy_, Apr 10 2017

%e a(4)=8 because pairs of factors are 1*4 and 2*2 and 1*4 + 2*2 = 8.

%t Table[ n * Ceiling[ DivisorSigma[0, n] /2 ], {n, 1, 73} ]

%o (MAGMA) [n*Ceiling(DivisorSigma(0, n)/2): n in [1..70]]; // _Vincenzo Librandi_, Apr 12 2017

%Y Cf. A060866.

%Y First differences of A083356.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, May 04 2001

%E More terms from _Robert G. Wilson v_, Jun 23 2001

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Last modified February 16 08:26 EST 2019. Contains 320159 sequences. (Running on oeis4.)