A392066 - OEIS

%I #15 Jan 07 2026 03:09:42

%S 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,

%T 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,

%U 2,0,0,0,2,3,0,0,5,2,0,0,0,2,3,0,0,2,0,0,0,2,0,3

%N 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}.

%C First differs from A063958 at n = 36.

%H Paolo Xausa, <a href="/A392066/b392066.txt">Table of n, a(n) for n = 1..10575</a> (rows 1..10000 of triangle, flattened).

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

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

%e Triangle begins:

%e   n\k|  1  2 ...

%e   --------------

%e    1 |  0;

%e    2 |  0;

%e    3 |  0;

%e    4 |  2;

%e    5 |  0;

%e    6 |  0;

%e    7 |  0;

%e    8 |  2;

%e    9 |  3;

%e   10 |  0;

%e   ...

%e   36 |  2, 3;

%e   37 |  0;

%e   38 |  0;

%e   39 |  0;

%e   40 |  2;

%e   ...

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

%t Array[A392066row, 100]

%Y Cf. A063958 (row sums).

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

%Y Cf. A035306, A056170, A071773.

%K nonn,tabf

%O 1,4

%A _Paolo Xausa_, Dec 30 2025