1,1

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 105-th power of the sum of its digits. A133509 gives n such that a(n) = 1. - Farideh Firoozbakht, Nov 23 2007

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.

M. L. Perez et al., eds., Smarandache Notions Journal

M. L. Perez et al., eds., Smarandache Notions Journal

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.

Cf. A061209, A061210, A046000, A076090, A046017.

Sequence in context: A053915 A067216 A076088 this_sequence A115988 A067506 A033119

Adjacent sequences: A061208 A061209 A061210 this_sequence A061212 A061213 A061214

nonn,base

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 21 2001

More terms from Ulrich Schimke, Feb 11, 2002

Edited by njas at the suggestion of Farideh Firoozbakht (mymontain(AT)yahoo.com), Dec 04 2007