A061210 Numbers which are the fourth powers of their digit sum.

0, 1, 2401, 234256, 390625, 614656, 1679616

Offset: 1

Author

Amarnath Murthy, Apr 21 2001

Keywords

• nonn
• fini
• full
• base

Comments

It can be shown that 1679616 = 36^4 is the largest such number.

Examples

			614656 = ( 6+1+4+6+5+6)^4 =28^4.
		

References

• Amarnath Murthy, The largest and the smallest m-th power whose digit sum is the m-th root. (To be published)
• Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 36.

Crossrefs

Cf. A061209 (with cubes), A061211.

Cf. A046000, A076090, A046017; A252648 and references there.

Programs

Mathematica

Select[Range[0,17*10^5],#==Total[IntegerDigits[#]]^4&] (* Harvey P. Dale, Sep 22 2019 *)

PARI

isok(n) = n == sumdigits(n)^4; \\ Michel Marcus, Jan 22 2015

Extensions

Corrected by Ulrich Schimke, Feb 11 2002

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