

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



FORMULA

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



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



