A225223 Primes of the form p - 1, where p is a practical number (A005153).

3, 5, 7, 11, 17, 19, 23, 29, 31, 41, 47, 53, 59, 71, 79, 83, 89, 103, 107, 127, 131, 139, 149, 167, 179, 191, 197, 199, 223, 227, 233, 239, 251, 263, 269, 271, 293, 307, 311, 347, 359, 367, 379, 383, 389, 419, 431, 439, 449, 461, 463, 467, 479, 499, 503, 509

Offset: 1

Author

Frank M Jackson, May 02 2013

Keywords

• nonn

Examples

			a(5)=17 as 18 is a practical number, 18-1=17 and it is the 5th such prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005153, A085498.

Programs

Mathematica

PracticalQ[n_] := Module[{f, p, e, prod = 1, ok = True}, If[n<1||(n>1&&OddQ[n]), False, If[n==1, True, f=FactorInteger[n]; {p, e}=Transpose[f]; Do[If[p[[i]]>1+DivisorSigma[1, prod], ok=False; Break[]]; prod=prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]];
Select[Table[Prime[n]+1, {n, 1, 200}], PracticalQ]-1 (* using T. D. Noe's program A005153 *)

PARI

isPractical(n)={
    if(n%2,return(n==1));
    my(f=factor(n),P=1);
    for(i=1,#f[,1]-1,
        P*=sigma(f[i,1]^f[i,2]);
        if(f[i+1,1]>P+1,return(0))
    );
    n>0
};
select(p->isPractical(p+1),primes(300)) \\ Charles R Greathouse IV, May 03 2013