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A373736
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a(n) = largest nondivisor k < n such that A007947(k) | n, or 0 if k does not exist.
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1
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0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 9, 0, 8, 9, 0, 0, 16, 0, 16, 9, 16, 0, 18, 0, 16, 0, 16, 0, 27, 0, 0, 27, 32, 25, 32, 0, 32, 27, 32, 0, 36, 0, 32, 27, 32, 0, 36, 0, 40, 27, 32, 0, 48, 25, 49, 27, 32, 0, 54, 0, 32, 49, 0, 25, 64, 0, 64, 27, 64, 0, 64, 0, 64, 45
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OFFSET
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1,6
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COMMENTS
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The number k does not exist for n in A000961, therefore we write a(n) = 0.
For n in A024619, a(n) is composite, since A007947(p) | n implies p | n for prime p.
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LINKS
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EXAMPLE
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Let rad = A007947 and let S(n) = {k <= n : rad(k) | n}, i.e., row n of A162306.
a(6) = 4 since 4 is the largest nondivisor k in S(6) = {1, 2, 3, 4, 6}.
a(10) = 8 since 8 is the largest nondivisor k in S(10) = {1, 2, 4, 5, 8, 10}.
a(15) = 9 since 9 is the largest nondivisor k in S(15) = {1, 3, 5, 9, 15}, etc.
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MATHEMATICA
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rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
Table[If[PrimePowerQ[n], 0, k = n - 1; Until[And[Divisible[n, rad[k]], ! Divisible[n, k]], k--]; k], {n, 2, 120}]
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PROG
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(PARI) rad(n) = factorback(factorint(n)[, 1]);
a(n) = forstep(k=n-1, 1, -1, if ((n % k) && !(n % rad(k)), return(k))); \\ Michel Marcus, Jun 18 2024
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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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