A202285 Numbers k such that the sum of digits^5 of k equals Sum_{d|k, 1

118678, 459385, 4150651, 4351003, 15033631, 20402671, 33224707, 35188159, 40460929, 42454261, 50067673, 54610051, 62004127, 77278261, 88720939, 106412347, 113660551, 113852653, 118203559, 121732873, 125252137, 128083639, 162748279, 163869049, 164863987

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 fifth powers of the digits of n is at most 9^5*log_10(n+1). Last term is a(404) = 23184988999. - Giovanni Resta, Oct 05 2018

Examples

			k=118678 is in the sequence because 1^5 + 1^5 + 8^5 + 6^5 + 7^5 + 8^5 = 90121, and the sum of the divisors 1 < d < k =  sigma(k) - k - 1 = 90121.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..404 (full sequence)

Crossrefs

Cf. A070308, A202279, A202147, A202240.

Programs

Mathematica

Q[n_]:=Module[{a=Total[Rest[Most[Divisors[n]]]]}, a == Total[IntegerDigits[n]^5]]; Select[Range[2, 10^7], Q]

Extensions

a(11)-a(25) and keywords fini and full added by Giovanni Resta, Oct 05 2018