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a(n) = Sum_{(d<n)|n} d*sigma(d).
2

%I #14 Sep 08 2022 08:46:08

%S 0,1,1,7,1,19,1,35,13,37,1,119,1,63,43,155,1,208,1,245,69,139,1,575,

%T 31,189,130,427,1,661,1,651,145,313,87,1274,1,387,195,1205,1,1155,1,

%U 959,520,559,1,2511,57,992,319,1309,1,1990,163,2115,393,877,1,4025

%N a(n) = Sum_{(d<n)|n} d*sigma(d).

%C If q are proper divisors of n then values of sequence a(n) are the bending moments at point 0 of static forces of sizes sigma(q) operating in places q on the cantilever as the nonnegative number axis of length n with support at point 0 by the schema: a(n) = Sum_{q | n} q*sigma(q).

%H Jaroslav Krizek, <a href="/A245484/b245484.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A001001(n) - A064987(n) = A064987(n) - A245773(n).

%F a(n) = 1 for n = primes.

%e For n=21 with proper divisors [1,3,7] we have: a(21) = 7*sigma(7) + 3*sigma(3) + 1*sigma(1) = 7*8 + 3*4 + 1*1 = 69.

%t a245484[n_Integer] := Total[#*DivisorSigma[1, #] & /@ Most[Divisors[n]]]; a245484 /@ Range[60] (* _Michael De Vlieger_, Aug 17 2014 *)

%o (Magma)[((&+[d*SumOfDivisors(d): d in Divisors(n)])-n*SumOfDivisors(n)): n in [1..1000]]

%Y Cf. A000203, A001001, A064987, A245773.

%K nonn

%O 1,4

%A _Jaroslav Krizek_, Aug 16 2014