A336681 - OEIS

%I #9 Jul 31 2020 06:46:34

%S 6485886225,71344748475,110260065825,123231838275,125730522225,

%T 149175383175,162485579025,185601564225,188090700525,191620685025,

%U 195686793225,201062472975,239977790325,265921335225,278893107675,304836652575,343751969925,395639059725,434554377075

%N Odd exponential admirable numbers: the odd terms of A336680.

%C 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).

%H Amiram Eldar, <a href="/A336681/b336681.txt">Table of n, a(n) for n = 1..65</a>

%e 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.

%t 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]

%Y The exponential version of A109729.

%Y Intersection of A005408 and A336680.

%Y Subsequence of A321147.

%Y Similar sequences: A329188, A334973, A334975.

%K nonn

%O 1,1

%A _Amiram Eldar_, Jul 30 2020