A066111 Prime powers m such that sigma_4(m^2)/sigma_2(m^2) is prime.

2, 3, 5, 13, 17, 31, 43, 61, 83, 109, 121, 125, 131, 229, 239, 257, 263, 269, 311, 313, 343, 361, 443, 463, 503, 571, 593, 599, 619, 641, 647, 653, 659, 701, 797, 811, 853, 953, 967, 1009, 1031, 1039, 1063, 1123, 1373, 1459, 1483, 1499, 1663, 1669, 1693

Offset: 1

Author

Labos Elemer, Dec 06 2001

Keywords

• nonn

Comments

Numbers m = p^w such that A001159(m^2)/A001157(m^2) is prime, i.e., m^2 is in A066109.

Also m is the square root of a term from A066109 (omitting the term 20). Apart from 20, up to 10000000 A066109 consists of squares of prime powers.

Examples

			m=125: m^2 = 15625 = A066109(13), sigma_4(15625) = 59700165039453751, sigma_2(15625) = 254313151, sigma_4/sigma_2 = 234750601 = A066110(13) is prime. Observe also that sigma_2 is close to sigma_4/sigma_2.
		

Links

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

Crossrefs

Cf. A001157, A001159, A066109, A066110.

Programs

PARI

isok(m) = isprimepower(m) && isprime(sigma(m^2, 4)/sigma(m^2, 2)); \\ Michel Marcus, Apr 06 2020