

A125115


Differences between consecutive abundant numbers.


6



6, 2, 4, 6, 6, 4, 2, 6, 6, 2, 4, 6, 4, 2, 6, 2, 4, 4, 2, 6, 4, 2, 2, 4, 4, 2, 6, 6, 6, 6, 2, 4, 6, 6, 4, 2, 6, 6, 2, 4, 6, 6, 4, 2, 2, 4, 4, 2, 6, 4, 2, 2, 4, 6, 6, 6, 6, 6, 2, 4, 6, 2, 4, 4, 2, 6, 6, 6, 4, 2, 2, 4, 6, 2, 4, 6, 6, 4, 2, 6, 2
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OFFSET

1,1


COMMENTS

One may think that a(n) is always even and greater than 1. This is not the case as can be seen with A096399 or A228382.  Michel Marcus, Aug 21 2013


LINKS

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


FORMULA

From Amiram Eldar, Oct 21 2020: (Start)
a(n) = A005101(n+1)  A005101(n).
Asymptotic mean: lim_{n>oo} (1/n) Sum_{k=1..n} a(k) = 1/A302991 = 4.0384... (End)


EXAMPLE

a(1) = 6 because 18  12 = 6; a(4) = 6 because 30  24 = 6.


MATHEMATICA

#[[2]]  #[[1]]&/@Partition[Select[Range[300], DivisorSigma[1, #] > 2# &], 2, 1] (* Harvey P. Dale, Dec 02 2006 *)
Differences[Select[Range[300], DivisorSigma[1, #] > 2# &]] (* Alonso del Arte, Apr 29 2019 *)


PROG

(PARI) lista(nn) = {lastab = 0; for (i=1, nn, if (sigma(i) > 2*i, if (lastab, print1(i  lastab, ", ")); lastab = i; ); ); } \\ Michel Marcus, Aug 21 2013
(GAP) A:=Filtered([1..350], n>Sigma(n)>2*n);; a:=List([1..Length(A)1], i>A[i+1]A[i]); # Muniru A Asiru, Jun 09 2018


CROSSREFS

Cf. A005101, A096399, A228382, A302991.
Sequence in context: A010493 A175286 A061496 * A202244 A257535 A020831
Adjacent sequences: A125112 A125113 A125114 * A125116 A125117 A125118


KEYWORD

easy,nonn


AUTHOR

Jason G. Wurtzel, Nov 21 2006


EXTENSIONS

More terms from Michel Marcus, Aug 21 2013


STATUS

approved



