A162840 Numbers k such that the cube of the sum of digits of k equals the product of digits of k.

0, 1, 666666, 1377789, 1377798, 1377879, 1377897, 1377978, 1377987, 1378779, 1378797, 1378977, 1379778, 1379787, 1379877, 1387779, 1387797, 1387977, 1389777, 1397778, 1397787, 1397877, 1398777, 1555888, 1558588, 1558858

Offset: 0

Author

Boris Hostnik (megpplus(AT)siol.net), Jul 14 2009

Keywords

• base
• nonn

Examples

			666666 is in the sequence because (1) cubed sum of its digits is (6+6+6+6+6+6)^3 = 46656, (2) the product of its digits is 6*6*6*6*6*6=46656; 46656=46656.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007954, A118880, A117720, A034710. - R. J. Mathar, Jul 19 2009

Programs

Maple

A007953 := proc(n) add(d,d=convert(n,base,10)) ; end: A007954 := proc(n) mul(d,d=convert(n,base,10)) ; end: A118880 := proc(n) (A007953(n))^3; end: for n from 1 to 2000000 do if A118880(n) = A007954(n) then printf("%d,\n",n) ; fi; od: # R. J. Mathar, Jul 19 2009

Mathematica

Select[Range[0,156*10^4],Total[IntegerDigits[#]]^3==Times@@IntegerDigits[#]&] (* Harvey P. Dale, Jul 07 2022 *)

Formula

{n: A118880(n)=A007954(n)}. - R. J. Mathar, Jul 19 2009