A317044 - OEIS

%I #14 Mar 15 2024 05:38:05

%S 1,2,3,4,6,7,8,9,11,12,13,14,17,18,20,21,24,25,26,27,29,30,33,34,35,

%T 36,38,39,40,41,44,45,47,48,49,50,52,53,56,57,58,59,62,63,65,66,69,70,

%U 71,72,74,75,79,80,82,83,86,87,88,89,91,92,93,94,96,97,98

%N Numbers k such that A(k+1) = A(k) + 1, where A() = A005100() are the deficient numbers.

%H Amiram Eldar, <a href="/A317044/b317044.txt">Table of n, a(n) for n = 1..10000</a>

%F Sequence is { k | A005100(k+1) = A005101(k) + 1 }.

%F Sequence is { k | A125238(k) = 1 }.

%p with(numtheory): A:=select(k->sigma(k)<2*k,[$1..150]):

%p   a:=select(j->A[j+1]=A[j]+1,[$1..nops(A)-1]);

%t Position[Differences[Select[Range[130], DivisorSigma[1, #] < 2*# &]], 1] // Flatten (* _Amiram Eldar_, Mar 15 2024 *)

%o (GAP) A:=Filtered([1..150],k->Sigma(k)<2*k);;  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+1);

%Y A317047 is the main sequence for this entry.

%Y Numbers k such that A(k+1) = A(k) + j, where A() = A005100() are the deficient numbers: this sequence (j=1), A317045 (j=2), A317046 (j=3).

%Y Cf. A005100, A125238.

%K nonn

%O 1,2

%A _Muniru A Asiru_, Aug 04 2018