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%I #15 Jul 20 2019 12:33:08
%S 3,11427,15503069909027,6,73,62531004125,85227106679780,20,15,
%T 71457130044805582612325294634331,56,47,16,33017,1138,68,23,19,762488,
%U 146,1552808,47,6234,32,45,2537,51700,54,426,83,34,40,3601,948281,531783519104,42,73,16493
%N Least number k which is not a divisor of n such that k^2 - n is a nonsquare powerful number.
%C De Koninck et al. calculated the first 50 terms of this sequence.
%H Amiram Eldar, <a href="/A309246/b309246.txt">Table of n, a(n) for n = 1..50</a>
%H Jean-Marie De Koninck, Nicolas Doyon, Florian Luca, and Michoacán Morelia, <a href="http://emis.ams.org/journals/JIS/VOL14/DeKoninck/dek.html">Powerful values of quadratic polynomials</a>, Journal of Integer Sequences, Vol. 14, No. 3 (2011), Article 11.3.3.
%F a(2) = 11427 since 11427^2 - 2 = 130576327 = 7^3 * 617^2 is a nonsquare powerful number, and k^2 - 2 is not a nonsquare powerful number for all k < 11427.
%o (PARI) is_a102834(n) = ispowerful(n) && !issquare(n) \\ after _Charles R Greathouse IV_ in A102834
%o a(n) = for(k=1, oo, if(n%k!=0 && is_a102834(k^2-n), return(k))) \\ _Felix Fröhlich_, Jul 19 2019
%Y Cf. A001694, A102834, A309245.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jul 18 2019
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