A394655 a(n) is the least common recursive multiple of {1, ..., n}.

1, 2, 6, 12, 60, 60, 420, 6720, 20160, 20160, 221760, 221760, 2882880, 2882880, 2882880, 184504320, 3136573440, 3136573440, 59594895360, 59594895360, 59594895360, 59594895360, 1370682593280, 1370682593280, 6853412966400, 6853412966400, 555126450278400

Offset

1,2

Comments

See A287958 for the definition of a recursive multiple.

The sequence increases only when n belongs to A164336 \ {1}, say n = p_1 ^ ... ^ p_k for k > 0 prime numbers p_1, ..., p_k; in that case, the prime tower factorization of a(n) equals that of a(n-1) plus an extra leaf p_k (see illustration in Links section).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..255

Rémy Sigrist, Illustration of initial terms

Index entries for sequences related to lcm's

Formula

a(n) = A287958(a(n-1), n) for n > 1.

a(n) >= A003418(n).

Example

See Links section.

Prog

(PARI) A287958(n, k) = if (n*k==0, return (max(n, k))); my (g=factor(lcm(n, k))); return (prod(i=1, #g~, g[i, 1]^A287958(valuation(n, g[i, 1]), valuation(k, g[i, 1]))))
{ v = 1; for (n = 1, 27, print1 (v = A287958(v, n)", "); ); }

Crossrefs

Cf. A003418, A164336 (indices of records), A287958.

Sequence in context: A109935 A347304 A065887 * A072181 A283487 A126915

Adjacent sequences: A394652 A394653 A394654 * A394656 A394657 A394658

Keyword

nonn

Author

Rémy Sigrist, Mar 27 2026

Status

approved