A394674 Irregular triangle T(n, k), n > 0, k = 1..A064372(n), read by rows; the n-th row corresponds to the minimal nonempty subset of A164336 with least common recursive multiple n.

1, 2, 3, 4, 5, 2, 3, 7, 8, 9, 2, 5, 11, 3, 4, 13, 2, 7, 3, 5, 16, 17, 2, 9, 19, 4, 5, 3, 7, 2, 11, 23, 3, 8, 25, 2, 13, 27, 4, 7, 29, 2, 3, 5, 31, 32, 3, 11, 2, 17, 5, 7, 4, 9, 37, 2, 19, 3, 13, 5, 8, 41, 2, 3, 7, 43, 4, 11, 5, 9, 2, 23, 47, 3, 16, 49, 2, 25

Offset

1,2

Comments

See A287958 for the definition of a recursive multiple.

This sequence has similarities with A141810; they differ when A001221(n) <> A064372(n); for example, for row n = 64 = 2^(2*3), A141810 contains 64 whereas the present sequence contains 4 and 8.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10001 (rows for n = 1..4278 flattened)

Index entries for sequences related to divisors

Example

Triangle T(n, k) begins:
  n     n-th row
  ----  ------------
     1  1
     2  2
     3  3
     4  4
     5  5
     6  2, 3
     7  7
     8  8
     9  9
    10  2, 5
    11  11
    12  3, 4
    13  13
    14  2, 7
    15  3, 5
    16  16
    17  17
    18  2, 9
    19  19
    20  4, 5

Prog

(PARI) row(n) = { my (r = []); if (n==1, r = [1], my (f = factor(n)); for (k = 1, #f~,
r = concat(r, apply (x -> f[k, 1]^x, row(f[k, 2]))); ); ); return (vecsort(r)); }

Crossrefs

Cf. A001221, A064372, A141810, A287958, A394673.

Sequence in context: A375636 A161768 A213925 * A141810 A141809 A309435

Adjacent sequences: A394670 A394671 A394673 * A394675 A394676 A394677

Keyword

nonn

Author

Rémy Sigrist, Mar 28 2026

Status

approved