A392066 Irregular triangle read by rows: row n lists the primes with exponent > 1 in the prime factorization of n. If no such primes exist, row n = {0}.

0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 5, 0, 3, 2, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 7, 5, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 0, 0, 3, 2, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 5, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 0, 3

Offset

1,4

Comments

First differs from A063958 at n = 36.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10575 (rows 1..10000 of triangle, flattened).

Formula

Sum_{k=1..max(A056170(n),1)} T(n,k) = A063958(n).

Product_{k=1..max(A056170(n),1)} max(T(n,k),1) = A071773(n).

Example

Triangle begins:
  n\k|  1  2 ...
  --------------
   1 |  0;
   2 |  0;
   3 |  0;
   4 |  2;
   5 |  0;
   6 |  0;
   7 |  0;
   8 |  2;
   9 |  3;
  10 |  0;
  ...
  36 |  2, 3;
  37 |  0;
  38 |  0;
  39 |  0;
  40 |  2;
  ...

Mathematica

A392066row[n_] := If[# == {}, {0}, #] & [Select[FactorInteger[n], Last[#] > 1 &][[All, 1]]];
Array[A392066row, 100]

Crossrefs

Cf. A063958 (row sums).

Cf. A392108 (minimum value in each row), A392109 (maximum value in each row).

Cf. A035306, A056170, A071773.

Sequence in context: A057108 A349435 A392108 * A392109 A063958 A349434

Adjacent sequences: A392063 A392064 A392065 * A392067 A392068 A392069

Keyword

nonn,tabf

Author

Paolo Xausa, Dec 30 2025

Status

approved