A083271 -id:A083271 - cp's OEIS frontend

A079449 Primes p such that there is at least one integer x satisfying p = x*tau(x)+1 where tau(x) = A000005(x), the number of divisors of x.

2, 5, 7, 11, 13, 23, 41, 47, 59, 61, 73, 83, 89, 107, 109, 137, 157, 167, 179, 193, 227, 229, 233, 241, 263, 271, 277, 313, 337, 347, 349, 359, 373, 379, 383, 409, 433, 449, 457, 461, 467, 479, 503, 563, 569, 587, 709, 719, 733, 809, 821, 839, 853, 857, 863

Offset: 1

Benoit Cloitre, Jan 13 2003

nonn

			12*tau(12) = 72 hence 73 is in the sequence.

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

Cf. A000005, A079448, A083271.

seq[lim_] := Union[Select[Table[k * DivisorSigma[0, k] + 1, {k, 1, Floor[lim/2]}], # <= lim && PrimeQ[#] &]]; seq[1000] (* Amiram Eldar, Apr 19 2025 *)

lista(nn) = {forprime(p=2, nn, for (n=1, p, if (n*numdiv(n)+1 == p, print1(p, ", "); break;);););} \\ Michel Marcus, Dec 01 2013

A083272 a(n) = ntau(a(n-1)) + 1 = nA000005(a(n-1)) + 1, a(0) = 1.

Original entry on oeis.org

1, 2, 5, 7, 9, 16, 31, 15, 33, 37, 21, 45, 73, 27, 57, 61, 33, 69, 73, 39, 81, 106, 89, 47, 49, 76, 157, 55, 113, 59, 61, 63, 193, 67, 69, 141, 145, 149, 77, 157, 81, 206, 169, 130, 353, 91, 185, 189, 385, 393, 201, 205, 209, 213, 217, 221, 225, 514, 233, 119, 241, 123, 249

Offset: 0

Labos Elemer, May 14 2003

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A000005, A083271.

h[x_] := x*DivisorSigma[0, h[x-1]]+1; h[0] = 1; Table[h[w], {w, 0, 100}]
nxt[{n_,a_}]:={n+1, (n+1)DivisorSigma[0,a]+1}; NestList[nxt,{0,1},70][[All,2]] (* Harvey P. Dale, Feb 06 2020 *)

A210495 Numbers n such that d(n)*n + 1 is prime, d(n) = number of divisors of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 10, 11, 12, 15, 18, 22, 23, 24, 27, 29, 30, 32, 34, 39, 41, 42, 45, 52, 53, 54, 56, 57, 58, 63, 64, 68, 69, 76, 83, 84, 87, 89, 93, 96, 108, 110, 113, 115, 131, 142, 144, 147, 150, 152, 153, 156, 162, 165, 168, 170, 172, 173, 175, 177

Offset: 1

Juri-Stepan Gerasimov, Jan 24 2013

nonn

This is the union of Sophie Germain primes and Sophie Germain nonprimes, so it might be called "Sophie Germain numbers".

Harvey P. Dale, Table of n, a(n) for n = 1..1000
J. S. Gerasimov, Sophie Germain nonprimes [title corrected], SeqFan mailing list, Jan 15 2013.

Cf. A083271, A005384, A209271, A000005.

A210495 := proc(n)
    option remember;
    local a;
    if n = 1 then
        1 ;
    else
        for a from procname(n-1)+1 do
            if isprime(numtheory[tau](a)*a+1) then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Jan 27 2013

Select[Range[200],PrimeQ[# DivisorSigma[0,#]+1]&] (* Harvey P. Dale, Aug 26 2013 *)

is(n)=isprime(numdiv(n)*n+1) \\ Charles R Greathouse IV, Jan 24 2013

cp's OEIS Frontend

A079449 Primes p such that there is at least one integer x satisfying p = x*tau(x)+1 where tau(x) = A000005(x), the number of divisors of x.

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A083272 a(n) = ntau(a(n-1)) + 1 = nA000005(a(n-1)) + 1, a(0) = 1.

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A210495 Numbers n such that d(n)*n + 1 is prime, d(n) = number of divisors of n.

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PARI

cp's OEIS Frontend

A079449 Primes p such that there is at least one integer x satisfying p = x*tau(x)+1 where tau(x) = A000005(x), the number of divisors of x.

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Author

Keywords

Examples

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Crossrefs

Programs

Mathematica

PARI

A083272 a(n) = n*tau(a(n-1)) + 1 = n*A000005(a(n-1)) + 1, a(0) = 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A210495 Numbers n such that d(n)*n + 1 is prime, d(n) = number of divisors of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A083272 a(n) = ntau(a(n-1)) + 1 = nA000005(a(n-1)) + 1, a(0) = 1.