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A261023
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Least number k such that prime(n) = sigma(k) - k - 1.
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2
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4, 9, 6, 10, 121, 22, 289, 34, 529, 841, 58, 1369, 30, 82, 2209, 42, 3481, 118, 4489, 5041, 70, 6241, 6889, 78, 9409, 10201, 202, 60, 214, 102, 16129, 17161, 18769, 84, 138, 298, 24649, 26569, 27889, 29929, 32041, 358, 36481, 238, 186, 394, 44521, 49729, 51529
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OFFSET
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1,1
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COMMENTS
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For any prime k <= p^2. In fact if k = p^2 we have that sigma(p) = sigma(p^2) - p^2, that is 1 + p = 1 + p + p^2 - p^2.
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LINKS
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FORMULA
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EXAMPLE
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sigma(2) = 3 and 4 is the least number such that sigma(4) - 4 = 7 - 4 = 3.
sigma(13) = 14 and 22 is the least number such that sigma(22) - 22 = 36 - 22 = 14.
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MAPLE
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with(numtheory): P:=proc(q) local a, k, n; for n from 1 to q do
if isprime(n) then for k from 1 to q do
if sigma(n)=sigma(k)-k then print(k); break; fi; od;
fi; od; end: P(10^9);
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MATHEMATICA
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Table[k = 1; While[DivisorSigma[1, Prime@ p] != DivisorSigma[1, k] - k, k++]; k, {p, 60}] (* Michael De Vlieger, Aug 07 2015 *)
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PROG
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(PARI) a(n) = my(k = 1, p = prime(n)); while(sigma(k)-k-1 != p, k++); k; \\ Michel Marcus, Aug 12 2015
(PARI) first(m)=my(v=vector(m), k); for(i=1, m, k=1; while(!(prime(i)==sigma(k)-k-1), k++); v[i]=k; ); v; \\ Anders Hellström, Aug 14 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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