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A062739
Odd powerful numbers.
19
1, 9, 25, 27, 49, 81, 121, 125, 169, 225, 243, 289, 343, 361, 441, 529, 625, 675, 729, 841, 961, 1089, 1125, 1225, 1323, 1331, 1369, 1521, 1681, 1849, 2025, 2187, 2197, 2209, 2401, 2601, 2809, 3025, 3087, 3125, 3249, 3267, 3375, 3481, 3721, 3969, 4225
OFFSET
1,2
COMMENTS
Smallest term of this sequence not also in A075109 is 675, followed by 1125. - Alonso del Arte, Nov 22 2011
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, B16
LINKS
W. A. Sentance, Occurrences of consecutive odd powerful numbers, Amer. Math. Monthly, 88 (1981), 272-274.
FORMULA
It is not true that a(n) = A001694(2n-1).
Sum_{n>=1} 1/a(n) = (2/3) * Sum_{n>=1} 1/A001694(n) = 2*zeta(2)*zeta(3)/(3*zeta(6)) = (2/3) * A082695 = 1.2957309... - Amiram Eldar, Jun 23 2020
EXAMPLE
Consecutive-odd examples from Sentance: {25,27},{70225,70227},{189750625,189750627}
MATHEMATICA
Powerful[n_Integer] := (n ==1) || Min[Transpose[FactorInteger[n]][[2]]]>=2; Select[Range[5000], OddQ[ # ]&&Powerful[ # ]&] (* T. D. Noe, May 04 2006 *)
Join[{1}, Select[Range[3, 4301, 2], Min[FactorInteger[#][[All, 2]]]>1&]] (* Harvey P. Dale, Jan 08 2021 *)
CROSSREFS
Cf. A076445 (consecutive odd powerful numbers).
Sequence in context: A020210 A275196 A325373 * A075109 A319165 A319152
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 12 2001
EXTENSIONS
Checked by T. D. Noe, May 04 2006
STATUS
approved