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

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

Offset: 0

Author

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

Keywords

• nonn

Comments

If p > 3 is prime, a(p) <= 14*p. - Robert Israel, Feb 21 2020

References

• 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).

Links

• Donovan Johnson, Table of n, a(n) for n = 0..10000 (first 1001 terms from T. D. Noe)
• 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].
• R. G. Wilson, V, Letter to N. J. A. Sloane, Jul. 1992.

Crossrefs

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

Programs

Maple

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:
Res; # Robert Israel, Feb 21 2020

Mathematica

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 *)

PARI

A007365(m)= {local(k,n); for(k=1,m,n=1; while(sigma(n)!=sigma(n+k), n++); print1(n,","))} \\ Klaus Brockhaus