A245484 a(n) = Sum_{(d<n)|n} d*sigma(d).

0, 1, 1, 7, 1, 19, 1, 35, 13, 37, 1, 119, 1, 63, 43, 155, 1, 208, 1, 245, 69, 139, 1, 575, 31, 189, 130, 427, 1, 661, 1, 651, 145, 313, 87, 1274, 1, 387, 195, 1205, 1, 1155, 1, 959, 520, 559, 1, 2511, 57, 992, 319, 1309, 1, 1990, 163, 2115, 393, 877, 1, 4025

Offset

1,4

Comments

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).

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Formula

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

a(n) = 1 for n = primes.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A001001, A064987, A245773.

Sequence in context: A098081 A125234 A028325 * A215503 A371835 A195220

Adjacent sequences: A245481 A245482 A245483 * A245485 A245486 A245487

Keyword

nonn

Author

Jaroslav Krizek, Aug 16 2014

Status

approved