|
| |
|
|
A007373
|
|
Numbers k such that sigma(k+2) = sigma(k).
(Formerly M5234)
|
|
19
|
|
|
|
33, 54, 284, 366, 834, 848, 918, 1240, 1504, 2910, 2913, 3304, 4148, 4187, 6110, 6902, 7169, 7912, 9359, 10250, 10540, 12565, 15085, 17272, 17814, 19004, 19688, 21410, 21461, 24881, 25019, 26609, 28124, 30592, 30788, 31484, 38210, 38982, 39786, 40310, 45354
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Numbers k such that antisigma(k+2) - antisigma(k) = 2*k + 3, where antisigma(m) = A024816(m) = sum of nondivisors of m. - Jaroslav Krizek, Mar 17 2013
|
|
|
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.
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp 12, Ellipses, Paris 2008.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
Zak Seidov and Donovan Johnson, Table of n, a(n) for n = 1..10000 (first 1000 terms from Zak Seidov)
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].
A. Weingartner, On the Solutions of sigma(n) = sigma(n+k), Journal of Integer Sequences, Vol. 14 (2011), #11.5.5.
R. G. Wilson, V, Letter to N. J. A. Sloane, Jul. 1992
|
|
|
MAPLE
|
A007373:=proc(q) local n;
for n from 1 to q do if sigma(n+2)=sigma(n) then print(n); fi; od; end:
A007373 (10^10); # Paolo P. Lava, Mar 25 2013
|
|
|
MATHEMATICA
|
Flatten[Position[Partition[DivisorSigma[1, Range[300000]], 3, 1], {x_, _, x_}]] (* Harvey P. Dale, Aug 08 2011 *)
SequencePosition[DivisorSigma[1, Range[300000]], {x_, _, x_}][[All, 1]] (* Harvey P. Dale, Nov 17 2022 *)
|
|
|
PROG
|
(PARI) je=[]; for(n=1, 10^5, a=sigma(n); b=sigma(n+2); if(a==b, je=concat(je, n))); je
|
|
|
CROSSREFS
|
Essentially the same as A055574.
Cf. A002961, A015861, A015863, A015865, A015866, A015867, A015876, A015877, A015880, A015881, A015882, A015883, A181647. [From Reinhard Zumkeller, Nov 03 2010]
Sequence in context: A204374 A261107 A211141 * A229254 A242957 A024628
Adjacent sequences: A007370 A007371 A007372 * A007374 A007375 A007376
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
|
|
|
EXTENSIONS
|
More terms from Jason Earls, Jul 20 2001
|
|
|
STATUS
|
approved
|
| |
|
|
