A394855 Numbers k such that prime tower factorizations of k and k+1 share some prime number.

8, 9, 24, 25, 39, 44, 45, 48, 49, 56, 62, 63, 74, 75, 80, 81, 87, 95, 98, 99, 104, 116, 117, 120, 121, 125, 135, 146, 147, 152, 153, 168, 169, 170, 171, 174, 175, 183, 200, 206, 207, 224, 225, 231, 244, 245, 248, 249, 255, 260, 261, 274, 275, 278, 279, 288

Offset

1,1

Comments

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

Two consecutive numbers, say k and k+1, cannot share a prime factor (since gcd(k, k+1) = 1). However, their prime tower factorizations can share some prime numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Illustration of initial terms

Formula

A284761(a(n)) <> 1.

Example

See Links section.

Prog

(PARI) A336965(n) = { my (f=factor(n), v=vecprod(f[, 1]~)); for (k=1, #f~, v=lcm(v, A336965(f[k, 2]))); v }
is(k) = gcd(A336965(k), A336965(k+1))!=1

Crossrefs

Cf. A182318, A284761, A286068 (a subsequence).

Sequence in context: A256932 A304600 A278076 * A389100 A081351 A032462

Adjacent sequences: A394852 A394853 A394854 * A394856 A394857 A394858

Keyword

nonn

Author

Rémy Sigrist, Apr 04 2026

Status

approved