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A046000 a(n) is largest number m equal to the sum of digits of m^n. 7
1, 9, 9, 27, 36, 46, 64, 68, 63, 81, 117, 108, 108, 146, 154, 199, 187, 216, 181, 207, 207, 225, 256, 271, 288, 337, 324, 307, 328, 341, 396, 443, 388, 423, 463, 477, 424, 495, 469, 523, 502, 432, 531, 572, 603, 523, 592, 666, 667, 695, 685, 685, 739, 746, 739, 683, 684, 802, 754, 845, 793, 833, 865 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cases a(n) = 0 (that is, values of n where m is not found) begin: 105, 164, 186, 194, 206, 216, 231, 254, 282, 285, ... - Jean-François Alcover, Jan 09 2018

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, 2003.

Amarnath Murthy, e-book, "Ideas on Smarandache Notions" MS.LIT

Joe Roberts, "Lure of the Integers", The Mathematical Association of America, 1992, p. 172.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A061211(n)^(1/n), for n > 0.

EXAMPLE

a(3) = 27 since 27^3 = 19683 and 1+9+6+8+3 = 27;

a(5) = 46 because 46 is largest number with 46^5 = 205962976, 2+0+5+9+6+2+9+7+6 = 46.

MATHEMATICA

meanDigit = 9/2; translate = 900; upperm[1] = translate;

upperm[n_] := Exp[-ProductLog[-1, -Log[10]/(meanDigit*n)]] + translate;

(* assuming that upper bound of m fits the implicit curve m = Log[10, m^n]*9/2 *)

a[0] = 1; a[n_] := (For[max = m = 0, m <= upperm[n], m++, If[m > 1 && m == Total[IntegerDigits[m^n]], max = m]]; max);

Table[a[n], {n, 0, 1000}] (* Jean-François Alcover, Jan 09 2018 *)

CROSSREFS

Cf. A046459, A046469, A046471, A055575, A055576, A055577, A046017.

Cf. A061211, A076090.

Cf. A152147 (table of m such that the sum of digits of m^n equals m).

Sequence in context: A059816 A111005 A076089 * A147378 A146604 A294691

Adjacent sequences:  A045997 A045998 A045999 * A046001 A046002 A046003

KEYWORD

base,nonn,nice

AUTHOR

David W. Wilson and Patrick De Geest

EXTENSIONS

More terms from Asher Natan Auel (auela(AT)reed.edu), Jun 01 2000

More terms from Franklin T. Adams-Watters, Sep 01 2006

Edited by N. J. A. Sloane at the suggestion of David Wasserman, Dec 12 2007

STATUS

approved

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Last modified July 20 14:01 EDT 2019. Contains 325181 sequences. (Running on oeis4.)