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A007365
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Smallest k such that sigma(n+k) = sigma(k).
(Formerly M4928)
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8
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1, 14, 33, 382, 51, 6, 20, 10, 15, 14, 21, 28, 35, 182, 24, 26, 30, 142, 40, 34, 42, 20, 57, 135, 70, 30, 99, 42, 66, 406, 88, 56, 60, 54, 93, 24, 105, 248, 147, 44, 63, 30, 80, 435, 114, 52, 196, 310, 140, 40, 105, 92, 160, 66, 120, 140, 105, 88, 352, 154
(list;
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listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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MAPLE
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N:= 1000: # to get all terms before the first with n + a(n) > N
S:= map(numtheory:-sigma, [$1..N]):
Res:= NULL:
found:= true:
for n from 1 while found do
found:= false;
for k from 1 to N-n do
if S[k] = S[k+n] then
Res:= Res, k; found:= true; break;
fi
od;
od:
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MATHEMATICA
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sk[n_]:=Module[{k=1}, While[DivisorSigma[1, k]!=DivisorSigma[1, n+k], k++]; k]; Array[sk, 60, 0] (* Harvey P. Dale, Oct 10 2012 *)
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PROG
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(PARI) A007365(m)= {local(k, n); for(k=1, m, n=1; while(sigma(n)!=sigma(n+k), n++); print1(n, ", "))} \\ Klaus Brockhaus
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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