A179657 Digital root of n-th practical number.

1, 2, 4, 6, 8, 3, 7, 9, 2, 6, 1, 3, 5, 9, 4, 6, 3, 9, 2, 6, 1, 3, 9, 6, 8, 3, 7, 9, 6, 1, 5, 9, 4, 3, 9, 2, 6, 5, 9, 6, 3, 7, 9, 6, 5, 9, 3, 7, 9, 2, 6, 1, 3, 9, 4, 8, 3, 9, 6, 9, 4, 8, 3, 9, 2, 6, 1, 9, 6, 3, 7, 9, 2, 6, 5, 9, 6, 3, 7, 9, 6, 1, 9, 4, 8, 9, 2, 6, 3, 5, 9, 4, 3, 9, 2, 6, 9, 8, 7, 9, 6, 1, 3, 5, 9

Offset: 1

Author

Jason G. Wurtzel, Jul 23 2010

Keywords

• nonn
• base

Examples

			For n=11, the 11th practical number is 28. As 2+8 = 10 and 1+0 = 1, the digital root is 1.
		

Crossrefs

Cf. A005153, A010888.

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]]]; Mod[ Select[ Range@ 500, PracticalQ], 9] /. {0 -> 9} (* Robert G. Wilson v, Aug 02 2010 *)

PARI

isok(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);
for(n=1, 1e3, if(isok(n), print1((n-1)%9+1", "))) \\ Altug Alkan, Nov 12 2015

Formula

a(n) = A010888(A005153(n)). - Michel Marcus, Nov 12 2015

Extensions

More terms from Robert G. Wilson v, Aug 02 2010