A376302 Smallest powerful m in row n of A064364, or -1 if none exist.

1, -1, -1, 4, -1, 8, -1, 16, 27, 25, -1, 64, 108, 49, 125, 200, 432, 196, 500, 392, 343, 121, 1323, 1225, 1372, 169, 2744, 968, 5488, 676, 3267, 1352, 1331, 289, 4563, 4225, 5324, 361, 2197, 2312, 21125, 1444, 7803, 2888, 17576, 529, 9747, 9025, 36125, 2116, 4913

Offset

1,4

Comments

Powerful numbers here refers to A001694.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..10766 (i.e., a(n) <= 2^40), ignoring negative values, showing perfect prime powers in red, and other powerful numbers in dark blue.

Example

First 13 rows of A064364 indicating the smallest powerful number in each row with brackets and other powerful numbers in parentheses. Rows 2, 3, 5, 7, and 11 do not have powerful numbers.
   n   Row n of A064364
  -------------------------------------------------
   1:  [1]
   2:   2
   3:   3
   4:  [4]
   5:   5    6
   6:  [8]  (9)
   7:   7   10   12
   8:  15  [16]  18
   9:  14   20   24 [27]
  10:  21  [25]  30   32  (36)
  11:  11   28   40   45   48   54
  12:  35   42   50   60  [64]  72  (81)
  13:  13   22   56   63   75   80   90   96  [108]

Mathematica

s = With[{nn = 40000}, Union@ Flatten@ Table[a^2*b^3, {b, Surd[nn, 3]},
  {a, Sqrt[nn/b^3]}]];
Insert[#, -1, Map[List, {2, 2, 3, 4, 7}]] &@
  s[[Values[#[[7 ;; 7 + LengthWhile[Differences@
  Keys[#][[7 ;; -1]], # == 1 &] ]] ][[All, 1]] ]] &@
  KeySort@ PositionIndex@
  Map[Total@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]] &, s]

Crossrefs

Cf. A001414, A001694, A064364, A363266 (largest squarefree m in row n of A064364).

Sequence in context: A295786 A080102 A106475 * A370614 A134829 A245966

Adjacent sequences: A376299 A376300 A376301 * A376303 A376304 A376305

Keyword

sign

Author

Michael De Vlieger, Sep 19 2024

Status

approved