A125115 Differences between consecutive abundant numbers.

6, 2, 4, 6, 6, 4, 2, 6, 6, 2, 4, 6, 4, 2, 6, 2, 4, 4, 2, 6, 4, 2, 2, 4, 4, 2, 6, 6, 6, 6, 2, 4, 6, 6, 4, 2, 6, 6, 2, 4, 6, 6, 4, 2, 2, 4, 4, 2, 6, 4, 2, 2, 4, 6, 6, 6, 6, 6, 2, 4, 6, 2, 4, 4, 2, 6, 6, 6, 4, 2, 2, 4, 6, 2, 4, 6, 6, 4, 2, 6, 2

Offset

1,1

Comments

One may think that a(n) is always even and greater than 1. This is not the case as can be seen with A096399 or A228382. - Michel Marcus, Aug 21 2013

Links

Muniru A Asiru, Table of n, a(n) for n = 1..10000

Formula

From Amiram Eldar, Oct 21 2020: (Start)

a(n) = A005101(n+1) - A005101(n).

Asymptotic mean: lim_{n->oo} (1/n) Sum_{k=1..n} a(k) = 1/A302991 = 4.0384... (End)

Example

a(1) = 6 because 18 - 12 = 6; a(4) = 6 because 30 - 24 = 6.

Mathematica

#[[2]] - #[[1]]&/@Partition[Select[Range[300], DivisorSigma[1, #] > 2# &], 2, 1] (* Harvey P. Dale, Dec 02 2006 *)
Differences[Select[Range[300], DivisorSigma[1, #] > 2# &]] (* Alonso del Arte, Apr 29 2019 *)

Prog

(PARI) lista(nn) = {lastab = 0; for (i=1, nn, if (sigma(i) > 2*i, if (lastab, print1(i - lastab, ", ")); lastab = i; ); ); } \\ Michel Marcus, Aug 21 2013
(GAP) A:=Filtered([1..350], n->Sigma(n)>2*n);;  a:=List([1..Length(A)-1], i->A[i+1]-A[i]); # Muniru A Asiru, Jun 09 2018

Crossrefs

Cf. A005101, A096399, A228382, A302991.

Sequence in context: A010493 A175286 A061496 * A202244 A257535 A020831

Adjacent sequences: A125112 A125113 A125114 * A125116 A125117 A125118

Keyword

easy,nonn

Author

Jason G. Wurtzel, Nov 21 2006

Extensions

More terms from Michel Marcus, Aug 21 2013

Status

approved