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%I #21 Aug 07 2022 16:43:46
%S 0,1,1073741824,205891132094649,1152921504606846976,
%T 931322574615478515625,221073919720733357899776,
%U 22539340290692258087863249,1237940039285380274899124224
%N 30th powers: a(n) = n^30.
%H Amiram Eldar, <a href="/A122971/b122971.txt">Table of n, a(n) for n = 0..10000</a>
%F 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 From _Amiram Eldar_, Oct 09 2020: (Start)
%F Dirichlet g.f.: zeta(s-30).
%F Sum_{n>=1} 1/a(n) = zeta(30) = 6892673020804*Pi^30/5660878804669082674070015625.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 536870911*zeta(30)/536870912 = 925118910976041358111*Pi^30/759790291646040068357842010112000000. (End)
%F Intersection of A000290 and A000578 and A000584. - _M. F. Hasler_, Jul 24 2022
%t Range[0,10]^30 (* _Harvey P. Dale_, Mar 06 2019 *)
%o (PARI) (A122971(n)=n^30); is_A122971(N)=ispower(N,30) _M. F. Hasler_, Jul 24 2022
%o (Python)
%o def A122971(n): return n**30
%o from sympy import nextprime
%o def is_A122971(N, k=30): # 2nd opt. arg to check for powers other than 30
%o p = 2
%o while N >= p**k:
%o for e in range(N):
%o if N % p: break
%o N //= p
%o if e % k: return False
%o p = nextprime(p)
%o return N < 2 # _M. F. Hasler_, Jul 24 2022
%Y Cf. A122968, A122969, A122970.
%Y Cf. A000290 (squares), A000578 (cubes), A000584 (5th powers).
%K mult,nonn,easy
%O 0,3
%A _Franklin T. Adams-Watters_, Oct 27 2006
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