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

1,2

Comments

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

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

Links

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

Example

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]

Prog

(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)) }

Crossrefs

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

Sequence in context: A129088 A086418 A100761 * A027748 A361650 A328852

Adjacent sequences: A336961 A336962 A336963 * A336965 A336966 A336967

Keyword

nonn,tabf

Author

Rémy Sigrist, Aug 09 2020

Status

approved