A392607 Squarefree numbers k such that A322582(k) <= A276085(k) <= A348507(k).

1, 2, 10, 15, 42, 2730, 5005, 34034, 36465, 51051, 461890, 570570, 646646, 692835, 6374082, 6760390, 8580495, 10140585, 10623470, 11741730, 15935205, 165889570, 170255085, 184848378, 190285095, 196051310, 248834355, 294076965, 308080630, 3646554366, 3932558630, 4360010655, 5142576670, 5277907635

Offset

1,2

Comments

No primorial numbers (A002110) larger than 2 are present. Proof: A322582(A002110(n)) = A053144(n) and A276085(A002110(n)) = A143293(n-1), and for n > 1, A053144(n) > A143293(n-1), as A002110(n) > A143293(n-1)+A005867(n), which follows because lim inf_{n->oo} A392860(n+1)/A392860(n) = prime(1+n)-1. See A392860.

The terms seem to have a prime factorization reminiscent of "primorials with holes", i.e., each have a dense run of prime factors, with just one or two primes from the middle (or prime 2 from the beginning) missing.

Notably, of the initial 34 terms, half (17) satisfy the condition A392594, while only five of them satisfy the conditions A391864 and A391865, those five being known squarefree terms of A369650.

Links

Table of n, a(n) for n=1..34.

Index entries for sequences related to primorial numbers.

Crossrefs

Intersection of A005117 and A392601.

Cf. A002110, A053144, A143293, A276085, A322582, A348507, A392860, A392861.

Cf. A369650, A391864, A391865, A392594.

Sequence in context: A369650 A392868 A181474 * A047187 A048043 A370115

Adjacent sequences: A392604 A392605 A392606 * A392608 A392609 A392610

Keyword

nonn

Author

Antti Karttunen, Jan 23 2026

Status

approved