A316099 - OEIS

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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

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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