

A316099


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


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

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



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

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


KEYWORD

nonn


AUTHOR



STATUS

approved



