A385288 Numbers with a prime number of prime factors, counted with multiplicity, and whose prime factors are each raised to a prime exponent.

4, 8, 9, 25, 27, 32, 49, 72, 108, 121, 125, 128, 169, 200, 243, 288, 289, 343, 361, 392, 500, 529, 675, 800, 841, 961, 968, 972, 1125, 1323, 1331, 1352, 1369, 1372, 1568, 1681, 1800, 1849, 2048, 2187, 2197, 2209, 2312, 2700, 2809, 2888, 3087, 3125, 3267, 3481

Offset

1,1

Comments

a(n) = A114129(n) through n=25; then a(26) = 961 and A114129(26) = 864.

Subset of A056166.

Subset of A001694. - Michael De Vlieger, Jun 25 2025.

Links

James C. McMahon, Table of n, a(n) for n = 1..1000

Example

200 = 2^3 * 5^2; 200 has a prime number of prime factors, counted with multiplicity (3 + 2 = 5), and exponents 3 and 2 are prime.

Mathematica

Select[Range[10^4], AllTrue[Last/@FactorInteger[#], PrimeQ]&&PrimeQ[PrimeOmega[#]]&]

Prog

(PARI) isok(k) = my(f=factor(k)); isprime(bigomega(k)) && (sum(k=1, #f~, isprime(f[k, 2])) == omega(f)); \\ Michel Marcus, Jun 25 2025

Crossrefs

Cf. A001248, A001694, A030078, A056166, A114129.

Sequence in context: A383211 A051676 A114129 * A383103 A053810 A076702

Adjacent sequences: A385285 A385286 A385287 * A385289 A385290 A385291

Keyword

nonn

Author

James C. McMahon, Jun 24 2025

Status

approved