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

Author

Jason G. Wurtzel, Nov 25 2006

Keywords

• easy
• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A005100, A094268, A125115, A318172.

Programs

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

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 *)

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