

A061209


Numbers which are the cubes of their digit sum.


12




OFFSET

1,3


COMMENTS

It can be shown that 19683 = (1 + 9 + 6 + 8 + 3)^3 = 27^3 is the largest such number.
Numbers of Dudeney.  Philippe Deléham, May 11 2013
If a number n has d digits, 10^(d1) <= n < 10^d, the cube of the digit sum is at most (d*9)^3 = 729*d^3; if d > 6 this is strictly smaller than 10^(d1) and cannot be equal to n. See also A061211.  M. F. Hasler, Apr 12 2015


REFERENCES

Amarnath Murthy, The largest and the smallest mth power whose digit sum is the mth root. (To be published)
H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1966, p. 36, #120


LINKS

Table of n, a(n) for n=1..7.
Wikipedia, Dudeney number


FORMULA

a(n) = A007953(a(n))^3.  M. F. Hasler, Apr 12 2015


EXAMPLE

4913 = (4 + 9 + 1 + 3)^3.


MATHEMATICA

Select[Range[20000], Total[IntegerDigits[#]]^3==#&] (* Harvey P. Dale, Apr 11 2015 *)


PROG

(PARI) for(n=0, 999999, sumdigits(n)^3==n&&print1(n", ")) \\ M. F. Hasler, Apr 12 2015


CROSSREFS

Cf. A007953, A061210, A061211, A252648.
Sequence in context: A186845 A239917 A114287 * A017259 A017367 A254899
Adjacent sequences: A061206 A061207 A061208 * A061210 A061211 A061212


KEYWORD

nonn,fini,full,base


AUTHOR

Amarnath Murthy, Apr 21 2001


EXTENSIONS

Initial term 0 added by M. F. Hasler, Apr 12 2015


STATUS

approved



