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A007365 Smallest k such that sigma(n+k) = sigma(k).
(Formerly M4928)

%I M4928

%S 1,14,33,382,51,6,20,10,15,14,21,28,35,182,24,26,30,142,40,34,42,20,

%T 57,135,70,30,99,42,66,406,88,56,60,54,93,24,105,248,147,44,63,30,80,

%U 435,114,52,196,310,140,40,105,92,160,66,120,140,105,88,352,154

%N Smallest k such that sigma(n+k) = sigma(k).

%C If p > 3 is prime, a(p) <= 14*p. - _Robert Israel_, Feb 21 2020

%D 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.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe and Donovan Johnson, <a href="/A007365/b007365.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from T. D. Noe).

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H R. G. Wilson, V, <a href="/A007015/a007015.pdf">Letter to N. J. A. Sloane, Jul. 1992</a>

%p N:= 1000: # to get all terms before the first with n + a(n) > N

%p S:= map(numtheory:-sigma, [$1..N]):

%p Res:= NULL:

%p found:= true:

%p for n from 1 while found do

%p found:= false;

%p for k from 1 to N-n do

%p if S[k] = S[k+n] then

%p Res:= Res, k; found:= true; break;

%p fi

%p od;

%p od:

%p Res; # _Robert Israel_, Feb 21 2020

%t 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 *)

%o (PARI) A007365(m)= {local(k,n); for(k=1,m,n=1; while(sigma(n)!=sigma(n+k), n++); print1(n,","))} \\ _Klaus Brockhaus_

%Y Cf. A065932, A065933. sigma(x)=A000203(x) is the sum of the divisors of x.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_

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Last modified September 23 09:03 EDT 2020. Contains 337298 sequences. (Running on oeis4.)