A245773 a(n) = n*sigma(n) - Sum_{(d<n)|n} d*sigma(d).

1, 5, 11, 21, 29, 53, 55, 85, 104, 143, 131, 217, 181, 273, 317, 341, 305, 494, 379, 595, 603, 653, 551, 865, 744, 903, 950, 1141, 869, 1499, 991, 1365, 1439, 1523, 1593, 2002, 1405, 1893, 1989, 2395, 1721, 2877, 1891, 2737, 2990, 2753, 2255, 3441, 2736, 3658

Offset

1,2

Comments

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

Sequence of numbers n such that a(n) = a(k) has solution for distinct numbers n and k: 314, 329, 411, 427, ...

Links

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

Formula

a(n) = 2*A064987(n) - A001001(n) = 2*n*sigma(n) - Sum_{d|n} d*sigma(d).

a(n) = A064987(n) - A245484(n).

a(n) > 1 for all n >= 1.

Example

For n=6 with divisors [1,2,3,6] we have: a(6) = 6*sigma(6)-(3*sigma(3)+2*sigma(2)+1*sigma(1) = 6*12-(3*4+2*3+1*1) = 53.

Maple

a:= proc(n) n * sigma(n) - add(d*sigma(d), d = divisors(n) minus {n}) end proc:
seq(a(n), n=1..100); # Robert Israel, Aug 17 2014

Mathematica

a245773[n_Integer] := n*DivisorSigma[1, n] - Total[#*DivisorSigma[1, #] & /@ Most[Divisors[n]]]; a245773 /@ Range[50] (* Michael De Vlieger, Aug 17 2014 *)

Prog

(Magma) [(2*(SumOfDivisors(n))-(&+[d*SumOfDivisors(d): d in Divisors(n)])): n in [1..1000]]

Crossrefs

Cf. A000203, A001001, A064987, A245484.

Sequence in context: A225376 A099400 A139534 * A166480 A164096 A298785

Adjacent sequences: A245770 A245771 A245772 * A245774 A245775 A245776

Keyword

nonn

Author

Jaroslav Krizek, Aug 16 2014

Status

approved