cp's OEIS Frontend

A062757 Denominator of sum of first n terms of the series 1/15 + 1/63 + 1/80 ... in which the denominators are perfect squares - 1 which are simultaneously other powers, e.g. a(1) = 15 because 16 = 4^2 = 2^4, a perfect square that is also a fourth power; hence 16-1 = 15 qualifies as a term.

%I A062757 #10 Jul 03 2025 18:31:41
%S A062757 15,315,5040,85680,278460,42840,14608440,540512280,10810245600,
%T A062757 46844397600,480155075400,145486987846200,17749412517236400,
%U A062757 5916470839078800,10769949084069775600,312328523438023492400
%N A062757 Denominator of sum of first n terms of the series 1/15 + 1/63 + 1/80 ... in which the denominators are perfect squares - 1 which are simultaneously other powers, e.g. a(1) = 15 because 16 = 4^2 = 2^4, a perfect square that is also a fourth power; hence 16-1 = 15 qualifies as a term.
%D A062757 W. Dunham, Euler: The Master of Us All, The Mathematical Association of America, Washington D.C., 1999, p. 65.
%D A062757 L. Euler, "Variae observationes circa series infinitas," Opera Omnia, Ser. 1, Vol. 14, pp. 216-244.
%H A062757 L. Euler, <a href="http://math.dartmouth.edu/~euler/pages/E072.html">Variae observationes circa series infinitas</a>
%e A062757 a(2)=63 because the perfect square 64= 8^2 = 4^3.
%t A062757 Table[ Denominator[ Plus@@(Take[ Select[ Range[ 2, 150 ], GCD@@(Last/@FactorInteger[ # ])>1& ]^2-1, k ]^-1) ], {k, 1, 16} ]
%Y A062757 Cf. A037450, A062834, A062965, A001597.
%K A062757 nonn
%O A062757 1,1
%A A062757 _Jason Earls_, Jul 16 2001
%E A062757 More terms from _Dean Hickerson_, Jul 24 2001