A125238 Differences between consecutive deficient numbers.

1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1

Offset

1,5

Comments

The first 3 occurs at n=4340. - R. J. Mathar, Jul 08 2015

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Formula

a(n) = A005100(n+1) - A005100(n).

Asymptotic mean: lim_{n->oo} (1/n) Sum_{k=1..n} a(k) = 1/A318172 = 1.3291... - Amiram Eldar, Oct 21 2020

Example

a(1) = 1 because 2-1 = 1.
a(5) = 2 because 7-5 = 2.

Maple

A125238 := proc(n)
    A005100(n+1)-A005100(n) ;
end proc: # R. J. Mathar, Jul 08 2015

Mathematica

Differences@ Select[Range@ 105, DivisorSigma[1, #] < 2 # &] (* Michael De Vlieger, Jun 29 2018 *)

Prog

(GAP) A:=Filtered([1..100], n->Sigma(n)<2*n);; a:=List([1..Length(A)-1], i->A[i+1]-A[i]); # Muniru A Asiru, Jun 26 2018

Crossrefs

Cf. A005100, A094268, A125115, A318172.

Sequence in context: A328511 A371245 A043278 * A025896 A050432 A343747

Adjacent sequences: A125235 A125236 A125237 * A125239 A125240 A125241

Keyword

easy,nonn

Author

Jason G. Wurtzel, Nov 25 2006

Status

approved