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A328235
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The least k > 0 such that the arithmetic derivative of n+k is a multiple of the arithmetic derivative of n.
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5
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1, 1, 4, 1, 15, 1, 12, 11, 8, 1, 4, 1, 13, 1, 12, 1, 20, 1, 24, 4, 23, 1, 56, 7, 10, 27, 36, 1, 28, 1, 44, 15, 114, 1, 76, 1, 84, 5, 56, 1, 48, 1, 20, 27, 53, 1, 80, 3, 36, 25, 76, 1, 81, 9, 4, 23, 26, 1, 116, 1, 64, 207, 80, 3, 52, 1, 40, 3, 82, 1, 232, 1, 205, 31, 36, 4, 27, 1, 92, 27, 88, 1, 160, 36, 130, 5, 12, 1, 81, 9, 52, 3
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OFFSET
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2,3
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LINKS
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EXAMPLE
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Arithmetic derivative of 6 is A003415(6) = 5. Not until at k=21 we find another number whose arithmetic derivative is a multiple of five (as A003415(21) = 10 = 2*5), thus a(6) = 21-6 = 15.
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PROG
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(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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