A373560 a(n) is the smallest multiple of prime(n)^2 that starts a run of 5 consecutive integers with 6 divisors, or -1 if no such multiple exists.

-1, -1, -1, 10093613546512321, -1, -1, 7700031346933907521, -1, 5344962129269790721, -1, 20453982425165652721, -1, 8163195338222675521, -1, 2467958104789157112721, -1, -1, -1, -1, 14666767069023896053921, 212170739123852995921, 287954235303137500060321, -1, 84769922583214545304321

Offset

1,4

Comments

Terms were obtained using the b-file at A141621.

a(n) = -1 if prime(n) is not in A001132.

Conjecture: the converse is also true.

Links

Table of n, a(n) for n=1..24.

Example

a(1) = a(2) = a(3) = -1 because the first of five consecutive integers having six divisors is never a multiple of 2^2, 3^2, or 5^2.
a(4) = 10093613546512321 because it is the smallest term in A141621 that is a multiple of prime(4)^2 = 49.
a(9) = 5344962129269790721 because it is the smallest term in A141621 that is a multiple of prime(9)^2 = 23^2.

Crossrefs

Cf. A001132, A030515, A042999, A054753, A141621.

Sequence in context: A329948 A160405 A162032 * A141621 A095432 A238358

Adjacent sequences: A373557 A373558 A373559 * A373561 A373562 A373563

Keyword

sign

Author

Jon E. Schoenfield, Jun 09 2024

Status

approved