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A244428 Sum of divisors of n and product of divisors of n are both perfect cubes. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 6 02:58 EDT 2022. Contains 355108 sequences. (Running on oeis4.)