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 A061211 Largest number m such that m is the n-th power of the sum of its digits. 9
 9, 81, 19683, 1679616, 205962976, 68719476736, 6722988818432, 248155780267521, 150094635296999121, 480682838924478847449, 23316389970546096340992, 2518170116818978404827136, 13695791164569918553628942336, 4219782742781494680756610809856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Clearly m = 1 always works, so a(n) exists for all n. - Farideh Firoozbakht, Nov 23 2007 105 is the smallest number n such that a(n)=1. This means that if n<105 there exists at least one number m greater than 1 such that m is the n-th power of the sum of its digits while 1 is the only number m such that m is the 105th power of the sum of its digits. A133509 gives n such that a(n) = 1. - Farideh Firoozbakht, Nov 23 2007 REFERENCES Amarnath Murthy, The largest and the smallest m-th power whose digits sum /product is its m-th root. To appear in Smarandache Notions Journal. Amarnath Murthy, e-book, "Ideas on Smarandache Notions", manuscript. LINKS T. D. Noe, Table of n, a(n) for n = 1..105 EXAMPLE a(3) = 19683 = 27^3 and no bigger number can have this property. (This has been established in the Murthy reference.) a(4) = 1679616 = (1+6+7+9+6+1+6)^4 = 36^4. MATHEMATICA meanDigit = 9/2; translate = 900; upperm = translate; upperm[n_] := Exp[-ProductLog[-1, -Log/(meanDigit*n)]] + translate; a[n_] := (For[max = m = 1, m <= upperm[n], m++, If[m == Total[ IntegerDigits[ m^n ] ], max = m]]; max^n); Array[a, 14] (* Jean-François Alcover, Jan 09 2018 *) CROSSREFS Cf. A061209, A061210, A046000, A076090, A046017. Sequence in context: A053915 A067216 A076088 * A115988 A067506 A263816 Adjacent sequences:  A061208 A061209 A061210 * A061212 A061213 A061214 KEYWORD nonn,base AUTHOR Amarnath Murthy, Apr 21 2001 EXTENSIONS More terms from Ulrich Schimke, Feb 11 2002 Edited by N. J. A. Sloane at the suggestion of Farideh Firoozbakht, Dec 04 2007 STATUS approved

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Last modified October 4 08:55 EDT 2022. Contains 357239 sequences. (Running on oeis4.)