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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
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
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].
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
KEYWORD
nonn
STATUS
approved