A227240 Numbers k such that sigma(k) divides sigma(2*k) and sigma(2*k + 1).

1, 3, 5, 7, 11, 23, 29, 41, 53, 77, 83, 89, 103, 113, 131, 143, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 533, 593, 641, 653, 659, 667, 683, 719, 743, 761, 807, 809, 817, 911, 953, 1013, 1019, 1031, 1049, 1073, 1103, 1223, 1229, 1289, 1409

Offset: 1

Author

Alex Ratushnyak, Jul 03 2013

Keywords

• nonn

Comments

Numbers such that 2*k and/or 2*k + 1 is also in the sequence: 1, 3, 5, 11, 41, 89, 179, 359, 509, 719, 743, ... (Cf. A007700).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000203, A007700, A058072, A058073.

Programs

Mathematica

Select[Range[1000], IntegerQ[DivisorSigma[1, 2#]/DivisorSigma[1, #]] && IntegerQ[DivisorSigma[1, 2# + 1]/DivisorSigma[1, #]] &] (* Alonso del Arte, Jul 15 2013 *)
Select[Range[1500],And@@Divisible[{DivisorSigma[1,2#],DivisorSigma[1,2#+1]}, DivisorSigma[1,#]]&] (* Harvey P. Dale, Feb 25 2016 *)

PARI

isok(n) = my(sn=sigma(n)); !(sigma(2*n) % sn) && !(sigma(2*n+1) % sn); \\ Michel Marcus, Oct 02 2017