The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A348601 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A348601

Nonexponential multiply-perfect numbers: numbers k such that k | A160135(k).
(history; published version)

#6 by N. J. A. Sloane at Mon Oct 25 11:11:28 EDT 2021

STATUS

proposed

approved

#5 by Amiram Eldar at Mon Oct 25 02:14:30 EDT 2021

STATUS

editing

proposed

#4 by Amiram Eldar at Mon Oct 25 02:06:47 EDT 2021

COMMENTS

The corresponding quotients A160135(k)/k are 0, 1, 1, 1, 1, 1, 2, 3, ...

EXAMPLE

1 is a term since it does not have nonexponential divisors, so A160135(1) = 0 which is divisible by 1.

#3 by Amiram Eldar at Mon Oct 25 01:45:54 EDT 2021

NAME

allocated for Amiram EldarNonexponential multiply-perfect numbers: numbers k such that k | A160135(k).

DATA

1, 6, 40, 234, 588, 89376, 10805558400

OFFSET

1,2

COMMENTS

The corresponding quotients A160135(k)/k are 0, 1, 1, 1, 1, 2, 3, ...

a(8) > 1.5*10^10, if it exists.

EXAMPLE

1 is a term since it does not have nonexponential divisors, so A160135(1) = 0 which is divisible by 1.

6 is a term since its nonexponential divisors are 1, 2 and 3, so A160135(6) = 1 + 2 + 3 = 6 which is divisible by 6.

40 is a term since its nonexponential divisors are 1, 2, 4, 5, 8 and 20, so A160135(40) = 1 + 2 + 4 + 5 + 8 + 20 = 40 which is divisible by 40.

MATHEMATICA

esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; Select[Range[1000], Divisible[DivisorSigma[1, #] - esigma[#], #] &]

CROSSREFS

Cf. A160135.

Similar sequences: A007691, A064594, A064595, A189000, A327158.

KEYWORD

allocated

nonn,more

AUTHOR

Amiram Eldar, Oct 25 2021

STATUS

approved

editing

#2 by Amiram Eldar at Mon Oct 25 01:40:56 EDT 2021

KEYWORD

allocating

allocated

#1 by Amiram Eldar at Mon Oct 25 01:40:56 EDT 2021

NAME

allocated for Amiram Eldar

KEYWORD

allocating

STATUS

approved