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A063519
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Least composite k such that phi(k+12n) = phi(k)+12n and sigma(k+12n) = sigma(k) + 12n where phi is the Euler totient function and sigma is the sum of divisors function.
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0
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65, 95, 341, 95, 161, 115, 629, 203, 145, 203, 365, 155, 185, 155, 301, 185, 329, 235, 1541, 287, 185, 287, 413, 205, 329, 215, 469, 215, 905, 371, 365, 305, 553, 371, 1037, 235, 1145, 623, 445, 371, 35249, 295, 1133, 371, 497, 515, 749, 413, 305, 671, 565
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OFFSET
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1,1
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COMMENTS
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No such simultaneous solutions were found if d=12n+6.
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LINKS
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FORMULA
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a(n) = Min{k: phi(k+12n) = phi(k)+12n and sigma(k+12n) = sigma(k)+12n and k is composite} with phi(k) = A000010(k) and sigma(k) = A000203(k).
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EXAMPLE
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a(97)=10217 because 10217 is composite, phi(10217)+1164 = 9600+1164 = 10764 = phi(11381) and sigma(10217)+1164 = 10836+1164 = 12000 = sigma(11381) with 1164 = 12*97 and there is no smaller composite with these properties.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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