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a(n) = the smallest number m with the smallest non-divisor n such that 1<n<m, or 0 if no such m exists.

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`%I #9 Aug 06 2024 02:05:47
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`%S 0,3,4,6,12,0,60,420,840,0,2520,0,27720,0,0,360360,720720,0,12252240,
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`%T 0,0,0,232792560,0,5354228880,0,26771144400,0,80313433200,0,
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`%U 2329089562800,72201776446800,0,0,0,0,144403552893600,0,0,0,5342931457063200,0,219060189739591200
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`%N a(n) = the smallest number m with the smallest non-divisor n such that 1<n<m, or 0 if no such m exists.
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`%F a(n) > 0 for prime powers n = p^k (p prime, k >= 1) else 0.
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`%F a(n) = A003418(n-1) for n = p^k > 3 (p prime, k >= 1). - _Amiram Eldar_, Aug 06 2024
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`%e a(7) = 60 because 60 is the smallest number such that numbers k < 7 divides 60 but number 7 is not divisor of 60.
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`%t a[n_] := If[PrimePowerQ[n], If[n <= 3, n+1, LCM @@ Range[n-1]], 0]; Array[a, 50] (* _Amiram Eldar_, Aug 06 2024 *)
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`%Y Cf. A003418, A199968, A199969.
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`%K nonn
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`%O 1,2
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`%A _Jaroslav Krizek_, Nov 26 2011
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`%E More terms from _Amiram Eldar_, Aug 06 2024
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