A283148 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.

8, 12, 27, 16, 20, 45, 125, 24, 28, 63, 175, 343, 32, 36, 81, 40, 44, 99, 275, 539, 1331, 48, 52, 117, 325, 637, 1573, 2197, 56, 60, 135, 64, 68, 153, 425, 833, 2057, 2873, 4913, 72, 76, 171, 475, 931, 2299, 3211, 5491, 6859, 80, 84, 189, 88, 92, 207, 575, 1127, 2783, 3887, 6647, 8303, 12167

Offset

2,1

Links

Michel Marcus, Rows n = 2..100 of triangle, flattened

Ana Rechtman, Février 2017, 4e défi, Images des Mathématiques, CNRS, 2017.

Example

Triangle begins:
8;
12, 27;
16,
20, 45, 125;
24;
28, 63, 175, 343;
32;
36, 81;
40;
44, 99, 275, 539, 1331;
48;
52, 117, 325, 637, 1573, 2197;
...

Mathematica

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

Prog

(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; }
tabf(nn) = for (n=2, nn, print(row(n))); \\ Michel Marcus, Mar 03 2017

Crossrefs

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

Cf. A126773, A283050, A283069, A283071.

Sequence in context: A067677 A045523 A006983 * A072327 A218558 A181735

Adjacent sequences: A283145 A283146 A283147 * A283149 A283150 A283151

Keyword

nonn,tabf

Author

Michel Marcus, Mar 01 2017

Status

approved