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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A010493 A175286 A061496 * A202244 A257535 A020831
KEYWORD
easy,nonn
AUTHOR
Jason G. Wurtzel, Nov 21 2006
EXTENSIONS
More terms from Michel Marcus, Aug 21 2013
STATUS
approved

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Last modified May 29 08:50 EDT 2024. Contains 372926 sequences. (Running on oeis4.)