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A288739
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Number of permutations without leading zeros of digits of n that have the same 2-adic value as n.
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0
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,13
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COMMENTS
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In searching for terms of A007602, one could search by product of digits; for example, numbers that have 6 as their product of digits include those whose digits consist only of one 6 and zero or more 1's and those that consist only of one 2, one 3, and zero or more 1's. 111132 is divisible by its product of digits. Knowing a(111132) might save some work in finding others like 311112. This idea holds for 5-smooth numbers; multiples of 7 need an extra trick.
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LINKS
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Table of n, a(n) for n=1..89.
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EXAMPLE
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a(109) = 2. The permutations of digits 109 and 901 have the same 2-adic value and no leading zeros.
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PROG
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(PARI) a(n) = {d = digits(n); nb = 1; padic = valuation(n, 2); for (k=1, (#d)!-1, p = numtoperm(#d, k); nd = vector(#d, k, d[p[k]]); if (nd[1] && (valuation(fromdigits(nd, 10), 2)) == padic, nb++); ); nb; } \\ Michel Marcus, Jul 02 2017
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CROSSREFS
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Cf. A007602, A007814.
Sequence in context: A221171 A333688 A319610 * A111621 A326398 A140195
Adjacent sequences: A288736 A288737 A288738 * A288740 A288741 A288742
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KEYWORD
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nonn,base,easy
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AUTHOR
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David A. Corneth, Jun 23 2017
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STATUS
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approved
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