login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A206852 Numbers N such that N/2 is a square, N/3 is a cube, and N/5 is a fifth power. 13
30233088000000, 32462531054272512000000, 6224724715037147546112000000, 34856377305871210027941888000000, 28156757354736328125000000000000000, 6683747269421867033919422988288000000, 681433858470444619689081338982912000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Georg Fischer, Table of n, a(n) for n = 1..1000

Shyam Sunder Gupta, Do you know, as of Feb 15 2012.

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).

FORMULA

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

MATHEMATICA

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

PROG

(PARI) {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

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

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

(Python)

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

CROSSREFS

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

Sequence in context: A297357 A080124 A121843 * A171264 A172574 A229069

Adjacent sequences: A206849 A206850 A206851 * A206853 A206854 A206855

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Feb 15 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 17:22 EST 2022. Contains 358421 sequences. (Running on oeis4.)