A033289 -id:A033289 - cp's OEIS frontend

A325847 Lesser of exponentially-odd amicable numbers pair: numbers m < k such that m = s(k) and k = s(m), where s(k) is the sum of proper exponential-odd divisors of k.

366, 3864, 16104, 16536, 59808, 71904, 142290, 142310, 196248, 198990, 240312, 326424, 341088, 348840, 366792, 520608, 664608, 704352, 753312, 912072, 1077890, 1156870, 1184490, 1511930, 1669910, 1805490, 1863456, 1936776, 2195640, 2236570, 2517480, 2686440

Offset: 1

Amiram Eldar, Sep 07 2019

nonn

The sum of proper exponential-odd divisors of k is A033634(k) - k if k is exponentially odd (A268335), or A033634(k) if not.

The larger counterparts are in A325848.

Amiram Eldar, Table of n, a(n) for n = 1..789 (terms below 10^10)

Cf. A033289, A033634, A268335, A325848.

f[e_] := If[OddQ[e], e + 2, e + 1]; fun[p_, e_] := 1 + (p^f[e] - p)/(p^2 - 1); a[1] = 1; a[n_] := Times @@ (fun @@@ (fct = FactorInteger[n])) - If[AllTrue[fct[[;; , 2]], OddQ], n, 0]; s = {}; Do[m = a[n]; If[m > n && a[m] == n, AppendTo[s, n]], {n, 1, 10^5}]; s

A325848 Larger of exponentially-odd amicable numbers pair: numbers m < k such that m = s(k) and k = s(m), where s(k) is the sum of proper exponential-odd divisors of k.

Original entry on oeis.org

378, 4584, 16632, 16728, 64032, 76704, 179118, 168730, 225096, 256338, 266568, 391656, 401952, 387720, 393528, 593952, 788448, 781728, 897888, 1052088, 1099390, 1292570, 1346598, 1598470, 2062570, 1863918, 2099424, 1940856, 2223720, 2429030, 2980056, 3336984

Offset: 1

Amiram Eldar, Sep 07 2019

nonn

The terms are ordered according to their lesser counterparts (A325847).

Amiram Eldar, Table of n, a(n) for n = 1..789 (terms with lesser counterparts below 10^10)

Cf. A033289, A033634, A268335, A325847.

f[e_] := If[OddQ[e], e + 2, e + 1]; fun[p_, e_] := 1 + (p^f[e] - p)/(p^2 - 1); a[1] = 1; a[n_] := Times @@ (fun @@@ (fct = FactorInteger[n])) - If[AllTrue[fct[[;; , 2]], OddQ], n, 0]; s = {}; Do[m = a[n]; If[m > n && a[m] == n, AppendTo[s, m]], {n, 1, 10^5}]; s

cp's OEIS Frontend

A325847 Lesser of exponentially-odd amicable numbers pair: numbers m < k such that m = s(k) and k = s(m), where s(k) is the sum of proper exponential-odd divisors of k.

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