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

1,2

Links

Table of n, a(n) for n=1..105.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A005153, A010888.

Sequence in context: A351330 A220102 A308080 * A239887 A354721 A355506

Adjacent sequences: A179654 A179655 A179656 * A179658 A179659 A179660

Keyword

nonn,base

Author

Jason G. Wurtzel, Jul 23 2010

Extensions

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

Status

approved