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A228061 Numbers n such that n^2 = sigma(m) for some m. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A191772 A323044 A057976

Adjacent sequences:  A228058 A228059 A228060 * A228062 A228063 A228064

KEYWORD

nonn

AUTHOR

T. D. Noe, Sep 04 2013

STATUS

approved

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Last modified June 26 05:13 EDT 2022. Contains 354877 sequences. (Running on oeis4.)