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Numbers n k such that the sum of digits^5 of n k equals the sum of Sum_{d|n, k, 1<d<nk} d.
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.
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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
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
Giovanni Resta, <a href="/A202285/b202285.txt">Table of n, a(n) for n = 1..404</a> (full sequence)
nonn,hard,base,fini,full
a(11)-a(25) and keywords fini and full added by Giovanni Resta, Oct 05 2018
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_Michel Lagneau (mn.lagneau2(AT)orange.fr), _, Dec 15 2011
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nonn,hard,new,base
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