A228061 Numbers k such that k^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

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: Inversion of Multiplicative Functions (invphi.gp).

Paul Pollack and Carl Pomerance, Square values of Euler's function, Bull. London Math. Soc., Vol. 46, No. 2 (2014), pp. 403-414; alternative link. 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 *)

Prog

(PARI) lista(kmax) = for(k = 1, kmax, if(invsigmaNum(k^2) > 0, print1(k, ", "))); \\ Amiram Eldar, Aug 12 2024, using Max Alekseyev's invphi.gp

Crossrefs

Cf. A000203, A038688 (squares 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