A323644 Numbers with 3 or 4 divisors.

4, 6, 8, 9, 10, 14, 15, 21, 22, 25, 26, 27, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205

Offset

1,1

Comments

Also numbers k such that the noncentral divisors of k are 1 and k.

Also numbers which are either semiprimes (A001358) or the cube of a prime (A030078). In other words: numbers which are either the product of two distinct primes (A006881) or the square of a prime (A001248) or the cube of a prime (A030078).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

4 is in the sequence because 4 has three divisors, they are 1, 2, 4. On the other hand, the noncentral divisors of 4 are 1 and 4, in accordance with the first comment.
6 is in the sequence because 6 has four divisors, they are 1, 2, 3, 6. On the other hand, the noncentral divisors of 6 are 1 and 6, in accordance with the first comment.

Mathematica

Select[Range[200], MemberQ[{3, 4}, DivisorSigma[0, #]] &] (* Amiram Eldar, Dec 03 2020 *)

Prog

(PARI) isok(n) = my(nd=numdiv(n)); (nd==3) || (nd==4); \\ Michel Marcus, Feb 26 2019

Crossrefs

Union of A001248 and A030513.

Cf. A001358, A006881, A030078, A161840, A323643.

Sequence in context: A373482 A346041 A341614 * A164702 A001745 A359982

Adjacent sequences: A323641 A323642 A323643 * A323645 A323646 A323647

Keyword

nonn,easy

Author

Omar E. Pol, Feb 26 2019

Status

approved