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A066073
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Composite numbers n such that sigma(n) - 1 is prime.
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14
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6, 10, 14, 15, 20, 21, 24, 26, 30, 33, 34, 35, 38, 40, 44, 46, 51, 52, 55, 57, 58, 60, 63, 65, 74, 76, 78, 84, 85, 86, 88, 90, 92, 93, 96, 105, 111, 114, 117, 118, 120, 123, 124, 126, 130, 135, 136, 141, 143, 145, 147, 153, 155, 158, 161, 164, 166, 168, 172, 174
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OFFSET
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1,1
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COMMENTS
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Composite numbers n such that sigma(n) = sigma(p) has a solution in the primes p. - Jaroslav Krizek, Feb 03 2012
Numbers n such that sigma(n) - 1 is greater than n and prime. - Giuseppe Coppoletta, Dec 22 2014
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LINKS
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EXAMPLE
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30, 46, 51, and 55 are in the sequence because each is a composite number n such that sigma(n)-1 = 71, which is prime; 71 itself is excluded from the sequence by definition.
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MAPLE
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filter:= proc(n)
local s;
s:= numtheory:-sigma(n)-1;
s > n and isprime(s);
end proc:
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MATHEMATICA
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Do[s=-1+DivisorSigma[1, m]; If[PrimeQ[s]&&!PrimeQ[m], Print[m]], {m, 1, 256}]
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PROG
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(Sage) [n for n in (2..174) if (sigma(n)-1).is_prime() and sigma(n)-1>n] # Giuseppe Coppoletta, Dec 22 2014
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CROSSREFS
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Cf. A000203, A058340, A066071, A066072, A066073, A066074, A066075, A066076, A066077, A066080, A248792.
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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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