A336964 Irregular triangle in which first row is 1, n-th row (n > 1) lists distinct prime numbers in the prime tower factorization of n.

1, 2, 3, 2, 5, 2, 3, 7, 2, 3, 2, 3, 2, 5, 11, 2, 3, 13, 2, 7, 3, 5, 2, 17, 2, 3, 19, 2, 5, 3, 7, 2, 11, 23, 2, 3, 2, 5, 2, 13, 3, 2, 7, 29, 2, 3, 5, 31, 2, 5, 3, 11, 2, 17, 5, 7, 2, 3, 37, 2, 19, 3, 13, 2, 3, 5, 41, 2, 3, 7, 43, 2, 11, 2, 3, 5, 2, 23, 47, 2, 3

Offset: 1

Author

Rémy Sigrist, Aug 09 2020

Keywords

• nonn
• tabf

Comments

The prime tower factorization of a number is defined in A182318.

The n-th row includes the n-th row of A027748.

Examples

			Triangle begins:
     1    [1]
     2    [2]
     3    [3]
     4    [2]
     5    [5]
     6    [2, 3]
     7    [7]
     8    [2, 3]
     9    [2, 3]
    10    [2, 5]
    11    [11]
    12    [2, 3]
    13    [13]
    14    [2, 7]
    15    [3, 5]
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10001 (rows for n = 1..4045)

Crossrefs

Cf. A027748, A115588 (row lengths), A182318, A336965.

Programs

PARI

row(n) = { my (f=factor(n), p=f[,1]~); for (k=1, #f~, if (f[k,2]>1, p=concat(p, row(f[k,2])));); if (#p==0, [1], Set(p)) }