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A007365 Smallest k such that sigma(n+k) = sigma(k).
(Formerly M4928)
8
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; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

T. D. Noe and 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

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A116150 A019272 A018949 * A065933 A276715 A115670

Adjacent sequences:  A007362 A007363 A007364 * A007366 A007367 A007368

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 14 06:07 EDT 2020. Contains 336477 sequences. (Running on oeis4.)