cp's OEIS Frontend

A122971 30th powers: a(n) = n^30.

%I A122971 #25 Oct 16 2024 14:40:09
%S A122971 0,1,1073741824,205891132094649,1152921504606846976,
%T A122971 931322574615478515625,221073919720733357899776,
%U A122971 22539340290692258087863249,1237940039285380274899124224
%N A122971 30th powers: a(n) = n^30.
%H A122971 Amiram Eldar, <a href="/A122971/b122971.txt">Table of n, a(n) for n = 0..10000</a>
%F A122971 Totally multiplicative sequence with a(p) = p^30 for prime p. Multiplicative sequence with a(p^e) = p^(30e). - _Jaroslav Krizek_, Nov 01 2009
%F A122971 From _Amiram Eldar_, Oct 09 2020: (Start)
%F A122971 Dirichlet g.f.: zeta(s-30).
%F A122971 Sum_{n>=1} 1/a(n) = zeta(30) = 6892673020804*Pi^30/5660878804669082674070015625.
%F A122971 Sum_{n>=1} (-1)^(n+1)/a(n) = 536870911*zeta(30)/536870912 = 925118910976041358111*Pi^30/759790291646040068357842010112000000. (End)
%F A122971 Intersection of A000290 and A000578 and A000584. - _M. F. Hasler_, Jul 24 2022
%t A122971 Range[0,10]^30 (* _Harvey P. Dale_, Mar 06 2019 *)
%o A122971 (PARI) (A122971(n)=n^30); is_A122971(N)=ispower(N,30) \\ _M. F. Hasler_, Jul 24 2022
%o A122971 (Python)
%o A122971 def A122971(n): return n**30
%o A122971 from sympy import nextprime
%o A122971 def is_A122971(N, k=30): # 2nd opt. arg to check for powers other than 30
%o A122971     p = 2
%o A122971     while N >= p**k:
%o A122971         for e in range(N):
%o A122971             if N % p: break
%o A122971             N //= p
%o A122971         if e % k: return False
%o A122971         p = nextprime(p)
%o A122971     return N < 2  #  _M. F. Hasler_, Jul 24 2022
%Y A122971 Cf. A122968, A122969, A122970.
%Y A122971 Cf. A000290 (squares), A000578 (cubes), A000584 (5th powers).
%K A122971 mult,nonn,easy
%O A122971 0,3
%A A122971 _Franklin T. Adams-Watters_, Oct 27 2006