A202147 Numbers k such that the sum of digits^4 of k equals Sum_{d|k, 1

1005, 5405, 89195, 92029, 107707, 149851, 323723, 524371, 610171, 999643, 1119253, 1134227, 1728787, 1900523, 2045171, 2170451, 2668381, 3351833, 3361717, 3611227, 5364059, 6571483, 7710883, 7865659, 8938691, 9286331, 9362051, 9593833, 10841387, 11507813

Offset: 1

Author

Michel Lagneau, Dec 15 2011

Keywords

• nonn
• base
• fini
• full

Comments

The sequence is finite because the restricted sum of divisors of n, for n composite, is at least sqrt(n), while the sum of the fourth powers of the digits of n is at most 9^4*log_10(n+1). Last term is a(101) = 163998389. - Giovanni Resta, Oct 05 2018

Examples

			1005 is in the sequence because 1^4 + 0^4 + 0^4 + 5^4 = 626, and the sum of the divisors 1< d<1005 is  3 + 5 +15 + 67 + 201+ 335 = 626.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..101 (full sequence)

Crossrefs

Cf. A070308, A202279, A202285, A202240.

Programs

Mathematica

Q[n_]:=Module[{a=Total[Rest[Most[Divisors[n]]]]}, a == Total[IntegerDigits[n]^4]]; Select[Range[2, 10^7], Q]

Extensions

Keywords fini and full added by Giovanni Resta, Oct 05 2018