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A053238
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First differences between numbers k for which sigma(k) > sigma(k+1).
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10
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2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2
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OFFSET
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1,1
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COMMENTS
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It seems that the expansion consists of only {1,2,3,4}.
The first exception is a(18360922) = 6, corresponding to the gap from 36721680 to 36721686. - Charles R Greathouse IV, Mar 09 2014
The asymptotic mean of this sequence is 2 (Erdős, 1936). - Amiram Eldar, Mar 19 2021
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LINKS
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FORMULA
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MAPLE
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with(numtheory): f := [seq( `if`((sigma(i) > sigma(i+1)), i, print( )), i=1..5000)];
seq( f[i+1] - f[i], i=1..2000);
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MATHEMATICA
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Differences[Select[Range[250], DivisorSigma[1, #]>DivisorSigma [1, #+1]&]] (* Harvey P. Dale, Apr 22 2011 *)
Differences[Flatten[Position[Partition[DivisorSigma[1, Range[300]], 2, 1], _?(#[[1]]>#[[2]]&), 1, Heads->False]]] (* Harvey P. Dale, Oct 18 2020 *)
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PROG
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(Haskell)
a053238 n = a053238_list !! (n-1)
a053238_list = zipWith (-) (tail a053226_list) a053226_list
(PARI) last=ls=1; for(n=2, 200, ns=sigma(n+1); if(ls<=ns, ls=ns; next); ls=ns; print1(n-last", "); last=n) \\ Charles R Greathouse IV, Mar 09 2014
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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