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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244428 Sum of divisors of n and product of divisors of n are both perfect cubes. 2

%I #22 Mar 11 2016 05:13:25

%S 1,1164,8148,11596,12028,28128,32980,34144,34528,36244,38764,39916,

%T 41164,41516,73200,75252,81172,84196,94023,100348,181948,182430,

%U 192175,193380,193612,194044,195780,196896,200574,204180,208416,211620,214176,217668,220116,225696,230860,235716

%N Sum of divisors of n and product of divisors of n are both perfect cubes.

%C This is also the intersection of A020477 and A048944.

%C Numbers m such that sigma(m) is a cube and (m is a cube or number of divisors of m is a multiple of 3). - _Chai Wah Wu_, Mar 10 2016

%H Chai Wah Wu, <a href="/A244428/b244428.txt">Table of n, a(n) for n = 1..500</a>

%e The divisors of 1164 are {1, 2, 3, 4, 6, 12, 97, 194, 291, 388, 582, 1164}. 1*2*3*4*6*12*97*194*291*388*582*1164 = 2487241979165915136 = 1354896^3 = (1164^2)^3. 1+2+3+4+6+12+97+194+291+388+582+1164 = 2744 = 14^3. Thus, since both the sum of divisors and the product of divisors are perfect cubes, 1164 is a member of this sequence.

%o (PARI) for(n=1,10^6,d=divisors(n);s=sum(i=1,#d,d[i]);p=prod(j=1,#d,d[j]);if(ispower(s,3)&&ispower(p,3),print1(n,", ")))

%o (Python)

%o from gmpy2 import iroot

%o from sympy import divisor_sigma

%o A244428_list = [i for i in range(1,10**4) if (iroot(i,3)[1] or not divisor_sigma(i,0) % 3) and iroot(int(divisor_sigma(i,1)),3)[1]] # _Chai Wah Wu_, Mar 10 2016

%Y Cf. A064710, A007955, A000203, A048944, A020477.

%K nonn

%O 1,2

%A _Derek Orr_, Jun 27 2014

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 March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)