A260698 Practical numbers of the form p - 1 where p is a prime.

1, 2, 4, 6, 12, 16, 18, 28, 30, 36, 40, 42, 60, 66, 72, 78, 88, 96, 100, 108, 112, 126, 150, 156, 162, 180, 192, 196, 198, 210, 228, 240, 256, 270, 276, 280, 306, 312, 330, 336, 348, 352, 378, 396, 400, 408, 420, 432, 448, 456, 460, 462, 486, 520, 522, 540, 546

Offset: 1

Author

Frank M Jackson, Nov 16 2015

Keywords

• nonn

Comments

Intersection of A005153 and A006093. - Michel Marcus, Nov 16 2015

Examples

			a(5)=12 as 12 is a practical number and 12+1=13 is prime. It is the 5th such practical number.
		

Crossrefs

Cf. A005153, A006093, A225223.

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] (* using T. D. Noe's program A005153 *)

PARI

is(n) = bittest(n, 0) && return(n==1); my(P=1); n && !for(i=2, #n=factor(n)~, n[1, i]>1+(P*=sigma(n[1, i-1]^n[2, i-1])) && return);
forprime(p=2, 1000, if(is(p-1), print1(p-1", "))) \\ Altug Alkan, Nov 16 2015