A336445 Integers m such that m/sopf(m) is a prime number where sopf(m) is A008472(m), the sum of the distinct primes dividing m.

4, 9, 25, 30, 49, 70, 84, 105, 121, 169, 231, 234, 260, 286, 289, 361, 456, 529, 532, 627, 646, 805, 841, 897, 961, 1116, 1364, 1369, 1581, 1665, 1681, 1798, 1849, 1924, 2064, 2150, 2209, 2632, 2809, 2967, 3055, 3339, 3481, 3526, 3721, 4489, 4543, 4824, 5025, 5041

Offset: 1

Author

Michel Marcus, Jul 22 2020

Keywords

• nonn

Comments

All squares of primes (A001248) are terms.

Examples

			4 is a term since sopf(4)=2 and 4/2 = 2 is a prime.
30 is a term since sopf(30)=10 and 30/10 = 3 is a prime.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..1049 (terms up to 10^7)

Crossrefs

Cf. A008472 (sopf).

Subsequence of A071139.

A001248 is a subsequence.

Cf. A336296, A336297.

Programs

PARI

sopf(n)=vecsum(factor(n)[, 1]); \\ A008472
isokp(k) = my(q=k/sopf(k)); (denominator(q)==1) && isprime(q);