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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A005153, A085498.

Sequence in context: A091305 A164319 A085498 * A346794 A226653 A128926

Adjacent sequences: A225220 A225221 A225222 * A225224 A225225 A225226

Keyword

nonn

Author

Frank M Jackson, May 02 2013

Status

approved