A228061 Numbers n such that n^2 = sigma(m) for some m.

1, 2, 6, 11, 12, 16, 18, 20, 24, 28, 30, 31, 32, 36, 40, 42, 44, 48, 52, 54, 56, 60, 62, 64, 66, 68, 70, 72, 76, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 108, 112, 114, 120, 124, 126, 128, 132, 136, 140, 144, 150, 152, 154, 156, 160, 162, 164, 168, 172, 174

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

P. Pollack and C. Pomerance, Square values of Euler's function, submitted for publication (2013). (See section 5.)

Formula

a(n) = sqrt(A038688(n)).

Mathematica

nn = 40000; t = Select[Union[DivisorSigma[1, Range[nn]]], IntegerQ[Sqrt[#]] &]; t = Sqrt[t]; t = Select[t, # < Sqrt[nn] &]
With[{nn=50000}, Union[Select[Sqrt[DivisorSigma[1, Range[nn]]], IntegerQ[ #] && #<=Sqrt[nn]&]]] (* Harvey P. Dale, Jul 12 2021 *)

Crossrefs

Cf. A038688 (square of these numbers).

Cf. A221284 (similar numbers for the phi function).

Sequence in context: A274689 A123112 A092189 * A357776 A191772 A323044

Adjacent sequences: A228058 A228059 A228060 * A228062 A228063 A228064

Keyword

nonn

Author

T. D. Noe, Sep 04 2013

Status

approved