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

0, 1, 1073741824, 205891132094649, 1152921504606846976, 931322574615478515625, 221073919720733357899776, 22539340290692258087863249, 1237940039285380274899124224

Offset: 0

Author

Franklin T. Adams-Watters, Oct 27 2006

Keywords

• mult
• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A122968, A122969, A122970.

Cf. A000290 (squares), A000578 (cubes), A000584 (5th powers).

Programs

Mathematica

Range[0,10]^30 (* Harvey P. Dale, Mar 06 2019 *)

PARI

(A122971(n)=n^30); is_A122971(N)=ispower(N,30) \\ M. F. Hasler, Jul 24 2022

Python

def A122971(n): return n**30
from sympy import nextprime
def is_A122971(N, k=30): # 2nd opt. arg to check for powers other than 30
    p = 2
    while N >= p**k:
        for e in range(N):
            if N % p: break
            N //= p
        if e % k: return False
        p = nextprime(p)
    return N < 2  #  M. F. Hasler, Jul 24 2022

Formula

Totally multiplicative sequence with a(p) = p^30 for prime p. Multiplicative sequence with a(p^e) = p^(30e). - Jaroslav Krizek, Nov 01 2009

From Amiram Eldar, Oct 09 2020: (Start)

Dirichlet g.f.: zeta(s-30).

Sum_{n>=1} 1/a(n) = zeta(30) = 6892673020804*Pi^30/5660878804669082674070015625.

Sum_{n>=1} (-1)^(n+1)/a(n) = 536870911*zeta(30)/536870912 = 925118910976041358111*Pi^30/759790291646040068357842010112000000. (End)

Intersection of A000290 and A000578 and A000584. - M. F. Hasler, Jul 24 2022