A241846 Numbers for which the cube of the sum of the digits is equal to the square of the product of their digits.

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

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

Michel Lagneau, Table of n, a(n) for n = 1..1419

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

Cf. A034710, A117720.

Sequence in context: A235026 A323612 A235019 * A064022 A116065 A234777

Adjacent sequences: A241843 A241844 A241845 * A241847 A241848 A241849

Keyword

nonn,base,fini,full

Author

Michel Lagneau, Apr 30 2014

Status

approved