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

Author

David W. Wilson, Sep 05 2009

Keywords

• base
• nonn

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.

Examples

			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.
		

Links

• David Wilson, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to powerful numbers

Crossrefs

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

Different from A007532 and A061862, which are variations.

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.