A066073 -id:A066073 - cp's OEIS frontend

A248793 Sigma(n) - 1 for n such that sigma(n) - 1 is prime.

2, 3, 5, 11, 7, 17, 11, 13, 23, 23, 17, 19, 41, 31, 23, 59, 41, 29, 71, 31, 47, 53, 47, 37, 59, 89, 41, 43, 83, 71, 47, 71, 97, 53, 71, 79, 89, 59, 167, 61, 103, 83, 67, 71, 73, 113, 139, 167, 79, 83, 223, 107, 131, 179, 89, 233, 167, 127, 251, 97, 101, 103

Offset: 1

Jaroslav Krizek, Nov 01 2014

a(n) = corresponding values of primes p = sigma(A248792(n)) - 1, where A248792(n) = numbers n such that sigma(n) - 1 is prime.

If there are at least two numbers k, h such that a(k) = a(h) = p, then p is in A158913.

Michael De Vlieger, Table of n, a(n) for n = 1..10000
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203, A000040, A066073, A248792.

[a: n in [1..1000] | IsPrime(a) where a is SumOfDivisors(n)-1]

F:= proc(n)
local r;
r:= numtheory:-sigma(n)-1;
if isprime(r) then r else NULL fi
end proc:
seq(F(n),n=1..1000); # Robert Israel, Nov 02 2014

a248793[n_Integer] :=
Cases[DivisorSigma[1, #] - 1 & /@ Range[n], ?PrimeQ]; a248793[104] (* _Michael De Vlieger, Nov 07 2014 *)

for(n=1,10^3,if(isprime(sigma(n)-1),print1(sigma(n)-1,", "))) \\ Derek Orr, Nov 01 2014

a(n) = A000203(A248792(n)) - 1.

If A248792(n) is a prime p, then a(n) = A248792(n) = p.

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

A128510 Composites c such that c*A001414(c) is adjacent to a prime.

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 14, 16, 20, 21, 25, 26, 28, 33, 34, 35, 36, 38, 40, 42, 44, 46, 50, 51, 52, 54, 55, 56, 60, 64, 65, 68, 72, 74, 76, 80, 81, 82, 85, 90, 93, 95, 96, 98, 100, 102, 110, 111, 115, 119, 121, 122, 123, 124, 126, 132, 133, 135, 138, 140, 143, 144, 145, 146, 148, 150

Offset: 1

J. M. Bergot, May 07 2007

The composites c of A002808 are multiplied by the sum of their prime factors (with multiplicity), and are placed into the sequence if that product is in A045718.

			c = 52= A002808(74) has prime factor sum A001414(52) = 17, and 52*17 = 883+1 is one away from the prime 883, which adds 52 to the sequence.

Cf. A066073.

A001414 := proc(n) local fcts,d ; fcts := ifactors(n)[2] ; add(op(1,d)*op(2,d),d=fcts) ; end proc:
isA045718 := proc(n) isprime(n+1) or isprime(n-1) ; end proc:
isA128510 := proc(n) local c; if not isprime(n) then c := n*A001414(n) ; isA045718(c) ; else false; end if ; end proc:
for n from 4 to 500 do if isA128510(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Nov 02 2009

8 inserted and sequence extended by R. J. Mathar, Nov 02 2009

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A248793 Sigma(n) - 1 for n such that sigma(n) - 1 is prime.

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

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A128510 Composites c such that c*A001414(c) is adjacent to a prime.

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