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A336681 Odd exponential admirable numbers: the odd terms of A336680. 1
6485886225, 71344748475, 110260065825, 123231838275, 125730522225, 149175383175, 162485579025, 185601564225, 188090700525, 191620685025, 195686793225, 201062472975, 239977790325, 265921335225, 278893107675, 304836652575, 343751969925, 395639059725, 434554377075 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Exponential admirable numbers that are odd are relatively rare: there are 5742336 even exponential admirable numbers that are smaller than the first odd term, i.e., a(1) = A336680(5742337).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..65

EXAMPLE

6485886225 is a term since 6485886225 = 80535 + 241605 + ... + (-8456175) + ... + 2161962075 is the sum of its proper exponential divisors with one of them, 8456175, taken with a minus sign.

MATHEMATICA

dQ[n_, m_] := (n > 0 && m > 0 && Divisible[n, m]); expDivQ[n_, d_] := Module[{ft = FactorInteger[n]}, And @@ MapThread[dQ, {ft[[;; , 2]], IntegerExponent[d, ft[[;; , 1]]]}]]; esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; expAdmQ[n_] := (ab = esigma[n] - 2*n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && expDivQ[n, ab/2]; Select[Range[1, 10^9, 2], expAdmQ]

CROSSREFS

The exponential version of A109729.

Intersection of A005408 and A336680.

Subsequence of A321147.

Similar sequences: A329188, A334973, A334975.

Sequence in context: A281222 A258365 A127342 * A268845 A161160 A242829

Adjacent sequences:  A336678 A336679 A336680 * A336682 A336683 A336684

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jul 30 2020

STATUS

approved

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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)