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
KEYWORD
nonn,base,fini,full
AUTHOR
Michel Lagneau, Apr 30 2014
STATUS
approved