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A191002
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Completely multiplicative function with a(prime(k)) = prime(k)*prime(k+1).
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11
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1, 6, 15, 36, 35, 90, 77, 216, 225, 210, 143, 540, 221, 462, 525, 1296, 323, 1350, 437, 1260, 1155, 858, 667, 3240, 1225, 1326, 3375, 2772, 899, 3150, 1147, 7776, 2145, 1938, 2695, 8100, 1517, 2622, 3315, 7560, 1763, 6930, 2021, 5148, 7875, 4002, 2491, 19440, 5929, 7350, 4845, 7956, 3127, 20250, 5005, 16632, 6555, 5394, 3599, 18900
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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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Sum_{n>=1} 1/a(n) = 1/Product_{k>=1} (1 - 1/(prime(k)*prime(k+1))) = 1.37660546... . - Amiram Eldar, Jan 07 2023
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MATHEMATICA
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f[p_, e_] := (p * NextPrime[p])^(e); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 04 2022 *)
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PROG
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(PARI) a(n)=local(fm); fm=factor(n); prod(k=1, matsize(fm)[1], (fm[k, 1]*nextprime(fm[k, 1]+1))^fm[k, 2])
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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