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

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

1,2

Comments

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

Links

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

Example

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.

Prog

(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, ", ")))
(Python)
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

Crossrefs

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

Sequence in context: A223875 A223849 A223800 * A221350 A227485 A252009

Adjacent sequences: A244425 A244426 A244427 * A244429 A244430 A244431

Keyword

nonn

Author

Derek Orr, Jun 27 2014

Status

approved