

A241846


Numbers for which the cube of the sum of the digits is equal to the square of the product of their digits.


2



0, 1, 88, 333, 11248, 11284, 11428, 11482, 11824, 11842, 12148, 12184, 12418, 12481, 12814, 12841, 14128, 14182, 14218, 14281, 14812, 14821, 18124, 18142, 18214, 18241, 18412, 18421, 21148, 21184, 21418, 21481, 21814, 21841, 24118, 24181, 24811, 28114
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OFFSET

1,3


COMMENTS

Let d_1 d_2... d_q denote the decimal expansion of a number n. The sequence lists the numbers n such that (d_1 + d_2 +...+ d_q)^3 = (d_1 * d_2 *...* d_q)^2.
The sequence is finite and contains 1419 terms because the maximum sum of the digits of a(n) is 16, the maximum product of the digits is 64 with 16^3 = 64^2 and the greatest number of the sequence is 2222221111.
The primitive values of a(n) (numbers whose decimal digits are not a permutation of another number of the sequence) are 0, 1, 88, 333, 11248, 112228, 1111444, 11112244, 111122224, 1111222222.
Nevertheless, the numbers 112228, 1111444, 11112244, 111122224, 1111222222 are not completely independent; for example, a decimal digit 4 of 1111444 becomes 22 and gives the number 11112244.


LINKS



EXAMPLE

333 is in the sequence because (3+3+3)^3 = (3*3*3)^2 = 729.
11248 is in the sequence because (1+1+2+4+8)^3 = (1*1*2*4*8)^2 = 4096.


MATHEMATICA

Select[Range[30000], (Plus @@ IntegerDigits[ # ]^3) == (Times @@ IntegerDigits[ # ]^2) &]


CROSSREFS



KEYWORD

nonn,base,fini,full


AUTHOR



STATUS

approved



