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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
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
1,2
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
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.
EXAMPLE
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.
PROG
(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
CROSSREFS
Cf. A002473. Subsequence of A238985.
Sequence in context: A280249 A096867 A100753 * A132416 A128606 A085123
KEYWORD
nonn,base
AUTHOR
Felix Huber, Jan 03 2023
STATUS
approved