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A361624
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Number of distinct prime factors in decimal concatenation of integer (n, n-1, ..., 2, 1, 2, ..., n-1, n) = A007942(n).
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2
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0, 2, 3, 2, 5, 3, 3, 4, 3, 3, 3, 3, 1, 4, 6, 2, 2, 3, 4, 7, 4, 8, 2, 3, 4, 6, 5, 7, 5, 6, 6, 3, 5, 7, 4, 5, 8, 5, 6, 6, 3, 3, 7, 7, 7, 7, 10, 7, 6, 6, 7, 4, 5, 5, 7
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OFFSET
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1,2
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COMMENTS
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a(n) < A360736(n) when n > 10 is a multiple of 4 or of 25, since, for these indices, A007942(n) is divisible by 2^2 or 5^2; but this inequality holds also, for other indices: for n = 6 (see example) and n = 39 where A007942(39) = 29 * 617^2 * 10185403128074353 * ...
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LINKS
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FORMULA
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EXAMPLE
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a(4) = 2 since 4321234 = 2 * 2160617;
a(6) = 3 since 65432123456 = 2^6 * 7 * 146053847.
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PROG
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(Python)
from sympy import primefactors
def A361624(n): return len(primefactors(int(''.join(map(str, range(n, 1, -1)))+''.join(map(str, range(1, n+1)))))) # Chai Wah Wu, Mar 21 2023
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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