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A225223 Primes of the form p - 1, where p is a practical number (A005153). 3
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 (list; graph; refs; listen; history; text; internal format)
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 * A226653 A128926 A139559

Adjacent sequences:  A225220 A225221 A225222 * A225224 A225225 A225226

KEYWORD

nonn

AUTHOR

Frank M Jackson, May 02 2013

STATUS

approved

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Last modified October 18 23:39 EDT 2019. Contains 328211 sequences. (Running on oeis4.)