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 A068916 Smallest positive integer that is equal to the sum of the n-th powers of its prime factors (counted with multiplicity). 3
 2, 16, 1096744, 3125, 256, 823543, 19683 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Does a(n) exist for all n? a(12)=65536, a(27)=4294967296. a(n) exists for all n of the form n=p^i-i, where p is prime and i > 0, since p^p^i is an example (see A067688 and A081177). - Jud McCranie, Mar 16 2003 a(23) <= 298023223876953125. a(24) <= 7625597484987. - Jud McCranie, Jan 18 2016 a(10) = 285311670611. - Jud McCranie, Jan 25 2016 a(24) = 7625597484987. - Jud McCranie, Jan 30 2016 LINKS S. P. Hurd and J. S. McCranie, Integers that are the Uniform Sum of Uniform Powers of all their Prime Factors, J. of Int. Seq., vol 22, article 19.3.4 EXAMPLE a(3) = 1096744 = 2^3*11^3*103; the sum of the cubes of the prime factors is 3*2^3 + 3*11^3 + 103^3 = 1096744. MATHEMATICA a[n_] := For[x=1, True, x++, If[x==Plus@@(#[]#[]^n&/@FactorInteger[x]), Return[x]]] PROG (PARI) isok(k, n) = {my(f=factor(k)); sum(j=1, #f~, f[j, 2]*f[j, 1]^n) == k; } a(n) = {my(k = 1); while(! isok(k, n), k++); k; } \\ Michel Marcus, Jan 25 2016 CROSSREFS Cf. A067688, A268036. Cf. A081177, A000325, A024024, A024050. Sequence in context: A092798 A258169 A325048 * A093987 A275588 A114560 Adjacent sequences:  A068913 A068914 A068915 * A068917 A068918 A068919 KEYWORD nonn,more AUTHOR Dean Hickerson, Mar 07 2002 STATUS approved

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Last modified July 24 03:01 EDT 2019. Contains 325290 sequences. (Running on oeis4.)