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 A062965 Positive numbers which are one less than a perfect square that is also another power. 2
 15, 63, 80, 255, 624, 728, 1023, 1295, 2400, 4095, 6560, 9999, 14640, 15624, 16383, 20735, 28560, 38415, 46655, 50624, 59048, 65535, 83520, 104975, 117648, 130320, 159999, 194480, 234255, 262143, 279840, 331775, 390624, 456975, 531440, 614655 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES W. Dunham, Euler: The Master of Us All, The Mathematical Association of America, Washington D.C., 1999, p. 65. L. Euler, "Variae observationes circa series infinitas," Opera Omnia, Ser. 1, Vol. 14, pp. 216-244. Fvss, Nicolao, "Demonstratio Theorematvm Qvorvndam Analyticorvm," Nova Acta Academiae Scientiarum Imperialis Petropolitanae, 8 (1794) 223-226. LINKS Leonard Euler, Variae observationes circa series infinitas Leonard Euler, Variae observationes circa series infinitas Eric Weisstein's World of Mathematics, Perfect Power FORMULA From Terry D. Grant, Oct 25 2020: (Start) a(n) = A001597(n+1)^2 - 1. Sum_{k>=1} 1/a(k) = 7/4 - Pi^2/6 = 7/4 - zeta(2). Sum_{k>=1} 1/(a(k)+1) = Sum_{k>=2} mu(k)*(1-zeta(2*k)). (End) EXAMPLE a(2)=63 because the perfect square 64 = 8^2 = 4^3. MATHEMATICA Take[ Select[ Range[ 2, 150 ], GCD@@(Last/@FactorInteger[ # ])>1& ]^2-1] (* corrected by Jon Maiga, Sep 28 2019 *) CROSSREFS Cf. A037450, A062834, A062757, A001597. Cf. A131605. Sequence in context: A067572 A066584 A065915 * A157968 A141759 A335574 Adjacent sequences:  A062962 A062963 A062964 * A062966 A062967 A062968 KEYWORD nonn AUTHOR Jason Earls, Jul 16 2001 EXTENSIONS More terms from Dean Hickerson, Jul 24 2001 STATUS approved

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Last modified September 23 02:26 EDT 2021. Contains 347609 sequences. (Running on oeis4.)