A226475 Numbers n such that sigma(n) + sigma(n+1) = sigma(n+2) + sigma(n+3).

75, 113, 295, 533, 686, 2130, 14805, 26966, 30235, 35095, 135653, 355675, 432996, 590138, 1214588, 2692853, 2952064, 3375195, 3486795, 5973014, 6880351, 7334956, 22266602, 25841659, 30483834, 37416582, 38390010, 40952513, 41109593, 57242145

Offset: 1

Author

Alex Ratushnyak, Jun 11 2013

Keywords

• nonn

Comments

Sigma(n) is the sum of the divisors of n: A000203.

Examples

			sigma(75) + sigma(76) = 124 + 140 = 264, and sigma(77) + sigma(78) = 96 + 168 = 264, so 75 is in the sequence.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..138 (terms < 10^13)

Crossrefs

Cf. A000203, A055574, A065900, A073500, A099632, A226361.

Programs

Mathematica

t = {}; s = DivisorSigma[1, Range[0, 3]]; n = 3; While[Length[t] < 10, n++; s = RotateLeft[s]; s[[4]] = DivisorSigma[1, n]; If[s[[1]] + s[[2]] == s[[3]] + s[[4]], AppendTo[t, n - 3]]]; t (* T. D. Noe, Jun 12 2013 *)
Module[{ds=DivisorSigma[1,Range[6*10^7]]},Flatten[Position[Partition[ds,4,1],?(Total[Take[#,2]]==Total[Take[#,-2]]&),{1},Heads->False]]] (* _Harvey P. Dale, Sep 13 2014 *)