A007373 Numbers k such that sigma(k+2) = sigma(k). (Formerly M5234)

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

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

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

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