A134703 Powerful numbers (2b): a sum of nonnegative powers of its digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 43, 63, 89, 132, 135, 153, 175, 209, 224, 226, 254, 258, 262, 263, 264, 267, 283, 308, 332, 333, 334, 347, 357, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 407, 445, 463, 472, 518, 538, 598, 629, 635, 653, 675, 730, 731, 732, 733, 734

Offset

1,3

Comments

Here 0 digits may be used, with the convention that 0^0 = 1. Of course 0^1 = 0, so one is free to use the 0 digit to get an extra 1, or not.

Links

David Wilson, Table of n, a(n) for n = 1..10000

Index entries for sequences related to powerful numbers

Formula

If n = d_1 d_2 ... d_k in decimal then there are integers m_1 m_2 ... m_k >= 0 such that n = d_1^m_1 + ... + d_k^m_k.

Example

43 = 4^2 + 3^3; 254 = 2^7 + 5^3 + 4^0 = 128 + 125 + 1.
209 = 2^7 + 0^1 + 9^2.
732 = 7^0 + 3^6 + 2^1.

Crossrefs

Cf. A001694, A005934, A005188, A003321, A014576, A023052, A046074.

Different from A007532 and A061862, which are variations.

Sequence in context: A116960 A126957 A228187 * A061862 A007532 A349279

Adjacent sequences: A134700 A134701 A134702 * A134704 A134705 A134706

Keyword

base,nonn

Author

David W. Wilson, Sep 05 2009

Status

approved