A066076 -id:A066076 - cp's OEIS frontend

A211658 Nonprime numbers k such that value of sigma(k) is unique; sigma(k) = A000203(k) = sum of divisors of k.

1, 4, 8, 9, 12, 18, 22, 27, 32, 36, 45, 49, 50, 64, 72, 81, 91, 98, 100, 106, 121, 128, 129, 133, 134, 146, 148, 152, 162, 169, 171, 192, 200, 202, 217, 218, 219, 243, 256, 259, 262, 268, 274, 288, 289, 292, 301, 314, 324, 333, 338, 343, 361, 381, 386, 388

Offset: 1

Jaroslav Krizek, Apr 20 2012

nonn

Complement of A066076 with respect to A211656.

			Number 36 is in the sequence because sigma(36) = 91 and there is no other number m with sigma(m) = 91.
Number 6 is not in the sequence because sigma(6) = 12 and 12 is also sigma(11).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000203, A066076, A211656, A211657, A211659, A211660.

A068014 Nonprimes n such that 1+phi(n) and -1 + sigma(n) are prime numbers.

Original entry on oeis.org

6, 10, 14, 21, 26, 34, 38, 40, 46, 55, 57, 58, 60, 63, 74, 76, 86, 88, 93, 111, 114, 117, 118, 124, 126, 135, 145, 153, 158, 166, 178, 184, 186, 190, 194, 198, 206, 208, 209, 216, 221, 224, 230, 232, 238, 250, 252, 254, 260, 266, 270, 278, 280, 295, 297, 298

Offset: 1

Labos Elemer, Feb 08 2002

nonn

1+A000010(n) and -1+A000203(n) are primes but n is nonprime.

			For n = 38, phi(38) + 1 = 19 and sigma(38) - 1 = 1 + 2 + 19 + 38 - 1 = 59. [corrected by _Peter Munn_, Dec 30 2017]

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A000010, A000203, A058339, A058340, A066071, A066072, A066073, A066074, A066075, A066076, A066077, A066080.

Do[s=-1+DivisorSigma[1, n]; s1=1+EulerPhi[n]; If[PrimeQ[s]&&PrimeQ[s1]&&!PrimeQ[n], Print[{n, s1, s}]], {n, 1, 1000}] (* generates sequence and related primes too *)
Select[Range@ 300, And[CompositeQ@ #, AllTrue[{1 + EulerPhi@ #, -1 + DivisorSigma[1, #]}, PrimeQ]] &] (* Michael De Vlieger, Dec 29 2017 *)

isok(n) = !isprime(n) && isprime(1+eulerphi(n)) && isprime(sigma(n)-1); \\ Michel Marcus, Dec 29 2017

cp's OEIS Frontend

A211658 Nonprime numbers k such that value of sigma(k) is unique; sigma(k) = A000203(k) = sum of divisors of k.

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