A122971 -id:A122971 - cp's OEIS frontend

A139571 Numbers with 31 divisors.

1073741824, 205891132094649, 931322574615478515625, 22539340290692258087863249, 17449402268886407318558803753801, 2619995643649944960380551432833049

Offset: 1

Omar E. Pol, May 07 2008

30th powers of primes. The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime.

Start of 31st row of A073915. - R. J. Mathar, Jun 27 2009, Jun 28 2009

T. D. Noe, Table of n, a(n) for n = 1..1000
OEIS Wiki, Index entries for number of divisors

Cf. A073915, A122971, A137493 (30 divs), A175742 (32 divs).

Prime[Range[11]]^30 (* Vladimir Joseph Stephan Orlovsky, May 05 2011 *)

a(n)=prime(n)^30 \\ Charles R Greathouse IV, Jun 19 2016

a(n) = A000040(n)^(31-1) = A000040(n)^30.

a(n) = A122971(A000040(n)). - R. J. Mathar, Jun 27 2009

A206852 Numbers N such that N/2 is a square, N/3 is a cube, and N/5 is a fifth power.

Original entry on oeis.org

30233088000000, 32462531054272512000000, 6224724715037147546112000000, 34856377305871210027941888000000, 28156757354736328125000000000000000, 6683747269421867033919422988288000000, 681433858470444619689081338982912000000

Offset: 1

M. F. Hasler, Feb 15 2012

The terms must be of the form N = 2^a*3^b*5^c*m^(2*3*5) where gcd(m, 2*3*5) = 1 and a-1, b-1 and c-1 must be a multiple of 2, 3 and 5, respectively, and a, b, c must be a multiple of the two other prime factors, respectively. This gives (a, b, c) == (3*5, 2*5, 2*3) [mod 2*3*5], whence N = 2^15*3^10*5^6*n^30. - M. F. Hasler, Jul 22 2022

Georg Fischer, Table of n, a(n) for n = 1..1000
Shyam Sunder Gupta, Do you know, as of Feb 15 2012.
Michael Penn, a sunny number puzzle!, YouTube video, 2021.
Index entries for linear recurrences with constant coefficients, signature (31, -465, 4495, -31465, 169911, -736281, 2629575, -7888725, 20160075, -44352165, 84672315, -141120525, 206253075, -265182525, 300540195, -300540195, 265182525, -206253075, 141120525, -84672315, 44352165, -20160075, 7888725, -2629575, 736281, -169911, 31465, -4495, 465, -31, 1).

Cf. A000290 (squares), A000578 (cubes), A000584 (5th powers), A122971 (30th powers).

Table[30233088000000 * n^30, {n,1,1000}] (* Georg Fischer, Feb 07 2021 *)

{is_A206852(n)=(n=divrem(n,3^10*5^6<<15))[2]==0 && ispower(n[1],30)} \\ replacing obsolete PARI code from 2012. - M. F. Hasler, Jul 22 2022

a(n)=30233088000000*n^30 \\ Charles R Greathouse IV, Apr 25 2012

def A206852(n): return 30233088000000*n**30 # M. F. Hasler, Jul 24 2022

def is_A206852(n):
    for p in (2, 3, 5):
        for e in range(n):
            if n % p: break
            n //= p
        if e % 30 != 30//p: return False
    return is_A122971(n) # M. F. Hasler, Jul 24 2022

a(n) = 30233088000000 * n^30 = 2^15 * 3^10 * 5^6 * n^30. - Charles R Greathouse IV, Apr 25 2012

A276377 60th powers: a(n) = n^60.

Original entry on oeis.org

0, 1, 1152921504606846976, 42391158275216203514294433201, 1329227995784915872903807060280344576, 867361737988403547205962240695953369140625, 48873677980689257489322752273774603865660850176

Offset: 0

Bhushan Bade, Sep 01 2016

Numbers which have square roots, cube roots, 4th, 5th and 6th roots.

Cf. A122971 (n^30), A183085 (subsequence).

[n^60: n in [0..10]]; // Bruno Berselli, Sep 03 2016

Range[0, 6]^60 (* Michael De Vlieger, Sep 02 2016 *)

a(n)=n^60 \\ Charles R Greathouse IV, Sep 01 2016

[n^60 for n in range(10)] # Bruno Berselli, Sep 03 2016

a(n) = n^60.

a(n) = A122971(n)^2. - Michel Marcus, Sep 02 2016

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A139571 Numbers with 31 divisors.

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A206852 Numbers N such that N/2 is a square, N/3 is a cube, and N/5 is a fifth power.

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A276377 60th powers: a(n) = n^60.

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Magma

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