A336681 Odd exponential admirable numbers: the odd terms of A336680.

6485886225, 71344748475, 110260065825, 123231838275, 125730522225, 149175383175, 162485579025, 185601564225, 188090700525, 191620685025, 195686793225, 201062472975, 239977790325, 265921335225, 278893107675, 304836652575, 343751969925, 395639059725, 434554377075

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