

A066111


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


2



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
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OFFSET

1,1


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.


LINKS

Table of n, a(n) for n=1..51.


EXAMPLE

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.


CROSSREFS

Cf. A001157, A001159, A066109, A066110.
Sequence in context: A284669 A154554 A105879 * A065820 A163268 A235624
Adjacent sequences: A066108 A066109 A066110 * A066112 A066113 A066114


KEYWORD

nonn


AUTHOR

Labos Elemer, Dec 06 2001


STATUS

approved



