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A351758
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a(n) = Sum_{p|n, p prime} Sum_{d|n} lcm(d,p).
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2
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0, 4, 6, 8, 10, 34, 14, 16, 15, 54, 22, 74, 26, 74, 76, 32, 34, 97, 38, 118, 104, 114, 46, 154, 35, 134, 42, 162, 58, 324, 62, 64, 160, 174, 164, 209, 74, 194, 188, 246, 82, 440, 86, 250, 220, 234, 94, 314, 63, 229, 244, 294, 106, 286, 252, 338, 272, 294, 118, 724, 122, 314
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OFFSET
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1,2
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LINKS
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FORMULA
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a(p) = 2*p, p prime.
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EXAMPLE
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a(6) = 34; a(6) = Sum_{p|6, p prime} Sum_{d|6} lcm(d,p) = Sum_{p|6, p prime} (lcm(1,p) + lcm(2,p) + lcm(3,p) + lcm(6,p)) = (lcm(1,2) + lcm(2,2) + lcm(3,2) + lcm(6,2)) + (lcm(1,3) + lcm(2,3) + lcm(3,3) + lcm(6,3)) = (2+2+6+6) + (3+6+3+6) = 34.
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PROG
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(PARI) a(n) = my(f=factor(n), d=divisors(f)); sum(k=1, #f~, sum(j=1, #d, lcm(d[j], f[k, 1]))); \\ Michel Marcus, Feb 19 2022
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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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