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A061209 Numbers which are the cubes of their digit sum. 12
0, 1, 512, 4913, 5832, 17576, 19683 (list; graph; refs; listen; history; text; internal format)
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^(d-1) <= 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^(d-1) and cannot be equal to n. See also A061211. - M. F. Hasler, Apr 12 2015

REFERENCES

H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1966, p. 36, #120.

Amarnath Murthy, The largest and the smallest m-th power whose digit sum is the m-th root. (To be published)

LINKS

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

Henk Koppelaar and Peyman Nasehpour, On Hardy's Apology Numbers, arXiv:2008.08187 [math.NT], 2020.

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

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Last modified November 25 05:43 EST 2020. Contains 338617 sequences. (Running on oeis4.)