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 A359412 Numbers with a record number of divisors that are both infinitary and exponential. 2
 1, 8, 216, 27000, 9261000, 12326391000, 27081081027000, 110924107886592000, 544970142046826496000, 3737950204299182936064000, 45479640135708158783090688000, 1109202943269786284560798789632000, 33044264882950203203350756741926912000, 1673791149116076642859325881248823873536000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Indices of records in A359411. a(2)-a(7) are the first 6 terms of A115964. The first 15 terms are cubes. Are there noncubes in this sequence? The corresponding record values are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, ... . Apparently, this sequence of records is the powers of 2 (A000079). LINKS Amiram Eldar, Table of n, a(n) for n = 1..15 MATHEMATICA s[n_] := DivisorSum[n, 1 &, BitAnd[n, #] == # &]; f[p_, e_] := s[e]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n]; v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq CROSSREFS Cf. A000079, A000578, A115964, A359411. Subsequence of A025487. Similar sequences: A037992, A318278. Sequence in context: A268471 A342598 A226524 * A115964 A245591 A247539 Adjacent sequences: A359409 A359410 A359411 * A359413 A359414 A359415 KEYWORD nonn AUTHOR Amiram Eldar, Dec 30 2022 STATUS approved

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Last modified April 16 08:27 EDT 2024. Contains 371698 sequences. (Running on oeis4.)