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A345304
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a(n) = Sum_{p|n, p prime} p * lcm(p,n/p).
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0
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0, 4, 9, 4, 25, 30, 49, 8, 9, 70, 121, 48, 169, 126, 120, 16, 289, 54, 361, 120, 210, 286, 529, 96, 25, 390, 27, 224, 841, 300, 961, 32, 462, 646, 420, 72, 1369, 798, 624, 240, 1681, 504, 1849, 528, 270, 1150, 2209, 192, 49, 150, 1020, 728, 2809, 162, 880, 448, 1254, 1798, 3481
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OFFSET
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1,2
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COMMENTS
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If p is prime, a(p) = Sum_{p|p} p * lcm(p,p/p) = p * p = p^2.
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LINKS
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EXAMPLE
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a(18) = Sum_{p|18} p * lcm(p,18/p) = 2*lcm(2,9) + 3*lcm(3,6) = 2*18 + 3*6 = 54.
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MATHEMATICA
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Table[Sum[k*LCM[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
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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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