A309245 Least number k > 0 which is not a divisor of n such that k^2 + n is a nonsquare powerful number (A102834).
682, 5, 37, 11, 1879706, 463, 11, 10, 2046, 341881, 31, 74, 70, 5519, 793, 22, 1952785824219551870, 57, 559, 338, 4580728614212333152148, 503259461, 45, 926, 190, 109, 36, 62, 436, 832836278711, 63, 88, 2451448196948930, 7037029, 36, 33
Offset: 1
Keywords
Examples
a(1) = 682 since 682^2 + 1 = 465125 = 5^3 * 61^2 is a nonsquare powerful number and is the smallest k > 0 such that k^2 + 1 is not a nonsquare powerful number.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..50
- Jean-Marie De Koninck, Nicolas Doyon, Florian Luca, and Michoacán Morelia, Powerful values of quadratic polynomials, Journal of Integer Sequences, Vol. 14, No. 3 (2011), Article 11.3.3.
Programs
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Mathematica
powerfulQ[n_] := Min@FactorInteger[n][[All, 2]] > 1; powerfulNonsquare[n_] := !IntegerQ[Sqrt[n]] && powerfulQ[n]; a[n_] := Module[{k=1}, While[Divisible[n, k] || !powerfulNonsquare[k^2 + n], k++]; k]; Table[a[n], {n, 1, 16}] -
PARI
is_a102834(n) = ispowerful(n) && !issquare(n) \\ after Charles R Greathouse IV in A102834 a(n) = for(k=1, oo, if(n%k!=0 && is_a102834(k^2+n), return(k))) \\ Felix Fröhlich, Jul 19 2019
Comments