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URL: https://oeis.org/A376302

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A376302
Smallest powerful m in row n of A064364, or -1 if none exist.
1
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, 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
KEYWORD
sign
AUTHOR
Michael De Vlieger, Sep 19 2024
STATUS
approved