cp's OEIS Frontend

A050150 Odd numbers with prime number of divisors.

%I A050150 #27 Jul 14 2024 05:06:32
%S A050150 3,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49,53,59,61,67,71,73,79,
%T A050150 81,83,89,97,101,103,107,109,113,121,127,131,137,139,149,151,157,163,
%U A050150 167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241
%N A050150 Odd numbers with prime number of divisors.
%C A050150 Here but not in A062090: [729, 15625, 59049, 117649, 531441]; in A062090 but not here: [1, 6561, 390625]. - _Klaus Brockhaus_, Nov 01 2001
%H A050150 T. D. Noe, <a href="/A050150/b050150.txt">Table of n, a(n) for n = 1..1000</a>
%F A050150 Numbers of the form p^e where p is an odd prime and e+1 is a prime.
%F A050150 A010051(A100995(a(n)) + 1) = 1. - _Reinhard Zumkeller_, Aug 16 2013
%F A050150 a(n) ~ n log n. - _Charles R Greathouse IV_, Aug 28 2013
%e A050150 Numbers of the form p^6 for example (such as 3^6 = 729) are here but not in A062090.
%t A050150 Select[ Range[1, 250, 2], PrimeQ[ Length[ Divisors[ # ]]] & ]
%t A050150 Select[Range[1,799,2],PrimeQ[DivisorSigma[0,#]]&] (* _Harvey P. Dale_, Jun 22 2011 *)
%o A050150 (PARI) forstep(n=1,1000,2, if(isprime(numdiv(n)),print1(n,",")))
%o A050150 (PARI) is(n)=n%2 && isprime(isprimepower(n)+1) \\ _Charles R Greathouse IV_, Aug 28 2013
%o A050150 (Haskell)
%o A050150 a050150 n = a050150_list !! (n-1)
%o A050150 a050150_list = filter ((== 1) . a010051 . (+ 1) . a100995) [1, 3 ..]
%o A050150 -- _Reinhard Zumkeller_, Aug 16 2013
%o A050150 (Python)
%o A050150 from sympy import divisor_count, isprime
%o A050150 def ok(n): return n and n%2 and isprime(divisor_count(n))
%o A050150 print([k for k in range(250) if ok(k)]) # _Michael S. Branicky_, Jul 05 2022
%Y A050150 Cf. A062090 (a different sequence).
%K A050150 easy,nonn,nice
%O A050150 1,1
%A A050150 _Jason Earls_, Jul 04 2001
%E A050150 More terms from _Jud McCranie_, Oct 31 2001