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

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

Author

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

Keywords

• nonn

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

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]

Programs

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 *)

PARI

je=[]; for(n=1,10^5,a=sigma(n); b=sigma(n+2); if(a==b,je=concat(je,n))); je

Extensions

More terms from Jason Earls, Jul 20 2001