A316099 Abundant numbers that differ from the next abundant number by 6.

12, 24, 30, 42, 48, 60, 72, 90, 114, 120, 126, 132, 144, 150, 162, 168, 180, 186, 210, 228, 234, 240, 246, 252, 264, 282, 288, 294, 312, 324, 330, 342, 354, 372, 384, 402, 408, 420, 426, 432, 450, 468, 480, 492, 504, 510, 522, 534, 552, 564, 582, 588, 594, 600

Offset

1,1

Comments

From Amiram Eldar, Sep 02 2022: (Start)

All the terms are even, since all the multiples of 6 that are larger than 6 are abundant numbers.

The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 8, 85, 865, 8716, 87668, 875528, 8761027, 87606693, 875947187, ... . Apparently, the asymptotic density of this sequence exists and equals 0.087... . (End)

Links

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

Example

12 is abundant, 13, 14, 15, 16 and 17 are deficient, 18 is abundant.
24 is abundant, 25, 26, 27, 28 and 29 are deficient, 30 is abundant.

Maple

with(numtheory):  A:=select(n->sigma(n)>2*n, [$1..800]): a:=seq(A[i], i in select(n->A[n+1]-A[n]=6, [$1..nops(A)-1]));

Mathematica

q[n_] := DivisorSigma[1, n] > 2 n; Select[Range[600], q[#] && SelectFirst[# + Range[6], q] == # + 6 &] (* Giovanni Resta, Jul 01 2018 *)

Prog

(GAP) A:=Filtered([1..800], n->Sigma(n)>2*n);;  a:=List(Filtered([1..Length(A)-1], i->A[i+1]-A[i]=6), j->A[j]);

Crossrefs

Subsequence of A005101.

Cf. A343302.

Cf. A231626, which has many common terms when 1 is subtracted.

Sequence in context: A108938 A085236 A068567 * A082801 A328587 A328632

Adjacent sequences: A316096 A316097 A316098 * A316100 A316101 A316102

Keyword

nonn

Author

Muniru A Asiru, Jun 25 2018

Status

approved