A064710 -id:A064710 - cp's OEIS frontend

A064121 Nonprime numbers n such that the sum of aliquot divisors of n (A001065) and product of aliquot divisors of n (A048741) are both perfect squares.

1, 12, 75, 76, 124, 147, 153, 176, 243, 332, 363, 477, 507, 524, 575, 688, 867, 892, 963, 1075, 1083, 1421, 1532, 1573, 1587, 1611, 1916, 2032, 2075, 2224, 2299, 2401, 2421, 2523, 2572, 2883, 2891, 3100, 3479, 3776, 3888, 4107, 4336, 4527, 4961, 4975

Offset: 1

Robert G. Wilson v, Oct 14 2001

Amiram Eldar, Table of n, a(n) for n = 1..10000

Variant of A064116. - R. J. Mathar, Oct 02 2008

Cf. A064710.

Select[ Range[5000], IntegerQ[ Sqrt[ Apply[ Plus, Delete[ Divisors[ # ], -1]]]] && IntegerQ[ Sqrt[ Apply[ Times, Delete[Divisors[ # ], -1]]]] && ! PrimeQ[ # ] & ]

A244428 Sum of divisors of n and product of divisors of n are both perfect cubes.

Original entry on oeis.org

1, 1164, 8148, 11596, 12028, 28128, 32980, 34144, 34528, 36244, 38764, 39916, 41164, 41516, 73200, 75252, 81172, 84196, 94023, 100348, 181948, 182430, 192175, 193380, 193612, 194044, 195780, 196896, 200574, 204180, 208416, 211620, 214176, 217668, 220116, 225696, 230860, 235716

Offset: 1

Derek Orr, Jun 27 2014

nonn

This is also the intersection of A020477 and A048944.

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

			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.

Chai Wah Wu, Table of n, a(n) for n = 1..500

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

Select[Range[236000],AllTrue[{CubeRoot[DivisorSigma[1,#]],CubeRoot[Times@@Divisors[#]]},IntegerQ]&] (* Harvey P. Dale, Nov 26 2024 *)

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,", ")))

from gmpy2 import iroot
from sympy import divisor_sigma
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

cp's OEIS Frontend

A064121 Nonprime numbers n such that the sum of aliquot divisors of n (A001065) and product of aliquot divisors of n (A048741) are both perfect squares.

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A244428 Sum of divisors of n and product of divisors of n are both perfect cubes.

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