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A253597
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Least Lucas-Carmichael number divisible by the n-th prime.
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3
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399, 935, 399, 935, 2015, 935, 399, 4991, 51359, 2015, 1584599, 20705, 5719, 18095, 2915, 46079, 162687, 22847, 46079, 16719263, 12719, 7055, 80189, 104663, 20705, 482143, 196559, 60059, 90287, 162687, 3441239, 13971671
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OFFSET
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2,1
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COMMENTS
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Has any odd prime number at least one Lucas-Carmichael multiple?
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 399 because this is the least Lucas-Carmichael number which is divisible by 3 (the second prime number).
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MATHEMATICA
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LucasCarmichaelQ[n_] := Block[{fi = FactorInteger@ n}, !PrimeQ@ n && Times @@ (Last@# & /@ fi) == 1 && Plus @@ Mod[n + 1, 1 + First@# & /@ fi] == 0]; f[n_] := Block[{k = p = Prime@ n}, While[ !LucasCarmichaelQ@ k, k += p]; k]; Array[f, 35, 2] (* Robert G. Wilson v, Feb 11 2015 *)
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PROG
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(PARI) is_A006972(n)=my(f=factor(n)); for(i=1, #f[, 1], if((n+1)%(f[i, 1]+1) || f[i, 2]>1, return(0))); #f[, 1]>1
a(n) = pn = prime(n); ln = 1; until (is_A006972(ln) && (ln % pn == 0), ln++); ln;
(PARI) is_A006972(n)=my(f=factor(n)); for(i=1, #f~, if((n+1)%(f[i, 1]+1) || f[i, 2]>1, return(0))); #f~>1
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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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