A378140 -id:A378140 - cp's OEIS frontend

A071277 a(1) = 1; a(n) = smallest palindrome which is a nontrivial product of n palindromes (repetitions allowed).

1, 4, 8, 88, 252, 2112, 2112, 2112, 4224, 8448, 48384, 48384, 405504, 405504, 405504, 40955904, 677707776, 677707776, 677707776, 677707776

Offset: 1

Amarnath Murthy, Jun 07 2002

			a(4) = 88 = 2*2*2*11.
a(5) = 252 = 2*2*3*3*7.

Cf. A071276, A378140.

Corrected and extended by Sascha Kurz, Jan 02 2003

Name corrected by Robert Israel, Jan 08 2025

A071276 a(1) = 1; a(n) = smallest palindrome which is a nontrivial product of n distinct palindromes.

Original entry on oeis.org

1, 6, 66, 252, 2112, 46464, 23677632, 880121088, 88892229888

Offset: 1

Amarnath Murthy, Jun 07 2002

			252=2*3*6*7 => a(4)=252.

Cf. A071277, A378140.

Corrected and extended by Sascha Kurz, Jan 02 2003
a(7)-a(8) from Sean A. Irvine, Jul 07 2024
a(9) from Michael S. Branicky, Jul 08 2024
Name corrected by Robert Israel, Jan 08 2025

A380657 Numbers whose prime factorization has more Pythagorean prime factors than non-Pythagorean prime factors (including multiplicities).

Original entry on oeis.org

5, 13, 17, 25, 29, 37, 41, 50, 53, 61, 65, 73, 75, 85, 89, 97, 101, 109, 113, 125, 130, 137, 145, 149, 157, 169, 170, 173, 175, 181, 185, 193, 195, 197, 205, 221, 229, 233, 241, 250, 255, 257, 265, 269, 275, 277, 281, 289, 290, 293, 305, 313, 317, 325, 337

Offset: 1

Clark Kimberling, Jan 30 2025

nonn

			50 appears because 2*5*5 has 2 Pythagorean prime factors but only 1 non-Pythagorean prime factor.

Cf. A000040, A002144, A002145, A083025, A376961, A377625, A378137, A378139, A378140.

f[{x_, y_}] := If[Mod[x, 4] == 1, y, -y];
s[n_] := Map[f, FactorInteger[n]];
p[n_] := {Total[Select[s[n], # > 0 &]], -Total[Select[s[n], # < 0 &]]};
p[1] = {0, 0};
t = Table[p[n], {n, 1, 500}];
u = Map[First, t];  (* A083025 *)
v = Map[Last, t] ;  (* A376961 *)
v - u (* A377625 *);
Flatten[Position[v - u, -1]]  (* this sequence *)

cp's OEIS Frontend

A071277 a(1) = 1; a(n) = smallest palindrome which is a nontrivial product of n palindromes (repetitions allowed).

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A071276 a(1) = 1; a(n) = smallest palindrome which is a nontrivial product of n distinct palindromes.

Views

Author

Keywords

Examples

Crossrefs

Extensions

A380657 Numbers whose prime factorization has more Pythagorean prime factors than non-Pythagorean prime factors (including multiplicities).

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica