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A072341
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a(n) = the least natural number k such that k*sigma(n) + 1 is prime.
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1
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1, 2, 1, 4, 1, 1, 2, 2, 4, 1, 1, 1, 2, 3, 3, 10, 1, 2, 2, 1, 3, 1, 3, 1, 10, 1, 1, 2, 1, 1, 3, 2, 2, 2, 2, 6, 5, 1, 2, 2, 1, 1, 2, 4, 1, 1, 2, 3, 4, 4, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 5, 1, 3, 4, 4, 3, 2, 1, 1, 3, 1, 6, 2, 2, 3, 2, 1, 2, 3, 2, 6, 1, 4, 2, 1, 3, 2, 1, 2, 4, 1, 2, 2, 3, 2, 3, 2, 12, 1, 6, 1, 2, 3
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OFFSET
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1,2
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COMMENTS
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Conjecture: a(n) is less than or equal to n for all n.
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LINKS
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FORMULA
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EXAMPLE
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sigma(4) = 7 and the least natural number k such that 7 k + 1 is prime is k = 4; so a(4) = 4.
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MATHEMATICA
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f[n_] := Module[{i}, i = 0; While[ ! PrimeQ[i*DivisorSigma[1, n] + 1], i++ ]; i]; Table[f[i], {i, 1, 150}]
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PROG
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(PARI) A072341(n) = { my(k=1, s=sigma(n)); while(!isprime(1+(k*s)), k++); k; }; \\ Antti Karttunen, Nov 07 2017
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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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