A359494 Zeroless numbers k which can be written as a product of the powers whose base is a digit of k and whose exponent is a nonnegative integer.

1, 2, 3, 4, 5, 6, 7, 8, 9, 25, 32, 36, 64, 125, 128, 135, 175, 216, 243, 256, 324, 375, 384, 432, 512, 625, 672, 729, 735, 784, 864, 875, 1296, 1372, 1715, 1764, 1792, 2592, 2744, 2916, 3125, 3375, 3456, 3645, 3675, 4375, 5832, 6144, 6272, 6912, 7776, 8192, 8575, 9216

Offset: 1

Author

Felix Huber, Jan 03 2023

Keywords

• nonn
• base

Comments

As this sequence is a subsequence of A238985 which is conjectured to be finite, this sequence is conjectured to be finite. - David A. Corneth, Jan 28 2023

This sequence seems to contain 11055 terms. - Felix Huber, Apr 11 2024

Examples

			672 is in the sequence via 672 = 6^2 * 7^1 * 2^4.
2592 is in the sequence via 2592 = 2^5 * 5^0 * 9^2 * 2^0.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..11055

Crossrefs

Cf. A002473. Subsequence of A238985.

Programs

PARI

is(n) = {if(n <= 1, return(n == 1)); my(d = Set(digits(n))); if(d[1] == 0, return(0)); d = setminus(d, Set(1)); forvec(x = vector(#d, i, [0, valuation(n, d[i])]), c = prod(i = 1, #d, d[i]^x[i]); if(c == n, return(1) ) ); 0 } \\ David A. Corneth, Jan 05 2023

Formula

Integers k = (x_1)^(m_1) * ... * (x_i)^(m_i) where x_j is the j-th digit of zeroless k and m_j is a nonnegative integer and 1 <= j <= i.