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A050150 Odd numbers with prime number of divisors. 9
3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Here but not in A062090: [729, 15625, 59049, 117649, 531441]; in A062090 but not here: [1, 6561, 390625]. - Klaus Brockhaus, Nov 01 2001

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

Numbers of the form p^e where p is an odd prime and e+1 is a prime.

A010051(a100995(a(n)) + 1) = 1. - Reinhard Zumkeller, Aug 16 2013

a(n) ~ n log n. - Charles R Greathouse IV, Aug 28 2013

EXAMPLE

Numbers of the form p^6 for example (such as 3^6 = 729) are here but not in A062090.

MATHEMATICA

Select[ Range[1, 250, 2], PrimeQ[ Length[ Divisors[ # ]]] & ]

Select[Range[1, 799, 2], PrimeQ[DivisorSigma[0, #]]&] (* Harvey P. Dale, Jun 22 2011 *)

PROG

(PARI) forstep(n=1, 1000, 2, if(isprime(numdiv(n)), print1(n, ", ")))

(PARI) is(n)=n%2 && isprime(isprimepower(n)+1) \\ Charles R Greathouse IV, Aug 28 2013

(Haskell)

a050150 n = a050150_list !! (n-1)

a050150_list = filter ((== 1) . a010051 . (+ 1) . a100995) [1, 3 ..]

-- Reinhard Zumkeller, Aug 16 2013

CROSSREFS

Cf. A062090 (a different sequence).

Sequence in context: A308838 A080429 A326581 * A062090 A172095 A309361

Adjacent sequences:  A050147 A050148 A050149 * A050151 A050152 A050153

KEYWORD

easy,nonn,nice

AUTHOR

Jason Earls, Jul 04 2001

EXTENSIONS

More terms from Jud McCranie, Oct 31 2001

STATUS

approved

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Last modified September 17 17:27 EDT 2019. Contains 327136 sequences. (Running on oeis4.)