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A309246 Least number k which is not a divisor of n such that k^2 - n is a nonsquare powerful number. 2
3, 11427, 15503069909027, 6, 73, 62531004125, 85227106679780, 20, 15, 71457130044805582612325294634331, 56, 47, 16, 33017, 1138, 68, 23, 19, 762488, 146, 1552808, 47, 6234, 32, 45, 2537, 51700, 54, 426, 83, 34, 40, 3601, 948281, 531783519104, 42, 73, 16493 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

De Koninck et al. calculated the first 50 terms of this sequence.

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.

FORMULA

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.

PROG

(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

CROSSREFS

Cf. A001694, A102834, A309245.

Sequence in context: A171363 A280655 A262651 * A055379 A047777 A195834

Adjacent sequences:  A309243 A309244 A309245 * A309247 A309248 A309249

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jul 18 2019

STATUS

approved

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Last modified December 4 17:32 EST 2021. Contains 349526 sequences. (Running on oeis4.)