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A340159
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a(n) is the smallest number m such that numbers m, m + 1, m + 2, ..., m + n - 1 have k, 2*k, 3*k, ..., n*k divisors respectively.
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5
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OFFSET
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1,3
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COMMENTS
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a(n) is the smallest number m such that tau(m) = tau(m + 1)/2 = tau(m + 2)/3 = tau(m + 3)/4 = ... = tau(m + n - 1)/n, where tau(k) = the number of divisors of k (A000005).
Corresponding values of tau(a(n)): 1, 1, 2, 2, 4, 4, 4, ...
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LINKS
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EXAMPLE
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a(3) = 61 because 61, 62 and 63 have 2, 4, and 6 divisors respectively and there is no smaller number having this property.
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PROG
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(PARI) isok(m, n) = {my(k=numdiv(m)); for (i=1, n-1, if (numdiv(m+i) != (i+1)*k, return (0)); ); return(1); }
a(n) = my(m=1); while(!isok(m, n), m++); m; \\ Michel Marcus, Dec 30 2020
(Python) # see LINKS
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CROSSREFS
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Cf. A294528 for similar sequence with primes.
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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