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Irregular triangle read by rows where the n-th row list the integers x such that the quotient x/(least prime factor of x)^2 is equal to n, for n>=2.
1

%I #17 Oct 19 2024 15:57:32

%S 8,12,27,16,20,45,125,24,28,63,175,343,32,36,81,40,44,99,275,539,1331,

%T 48,52,117,325,637,1573,2197,56,60,135,64,68,153,425,833,2057,2873,

%U 4913,72,76,171,475,931,2299,3211,5491,6859,80,84,189,88,92,207,575,1127,2783,3887,6647,8303,12167

%N Irregular triangle read by rows where the n-th row list the integers x such that the quotient x/(least prime factor of x)^2 is equal to n, for n>=2.

%H Michel Marcus, <a href="/A283148/b283148.txt">Rows n = 2..100 of triangle, flattened</a>

%H Ana Rechtman, <a href="http://images-archive.math.cnrs.fr/Fevrier-2017-4e-defi.html">Février 2017, 4e défi</a>, Images des Mathématiques, CNRS, 2017.

%e Triangle begins:

%e 8;

%e 12, 27;

%e 16,

%e 20, 45, 125;

%e 24;

%e 28, 63, 175, 343;

%e 32;

%e 36, 81;

%e 40;

%e 44, 99, 275, 539, 1331;

%e 48;

%e 52, 117, 325, 637, 1573, 2197;

%e ...

%t Table[Select[Range[n^3], #/(FactorInteger[#][[1, 1]])^2 == n &], {n, 2, 23}] // Flatten (* _Michael De Vlieger_, Mar 02 2017 *)

%o (PARI) row(n) = {vn = []; for(k=2, n^3, if (!(k % (p=factor(k)[1,1]^2)) && (k/p == n), vn = concat(vn, k));); vn;}

%o tabf(nn) = for (n=2, nn, print(row(n))); \\ _Michel Marcus_, Mar 03 2017

%Y Cf. A055396 (number of terms of the n-th row).

%Y Cf. A126773, A283050, A283069, A283071.

%K nonn,tabf

%O 2,1

%A _Michel Marcus_, Mar 01 2017