A126805 "Class-" (or "class-minus") number of prime(n) according to the Erdős-Selfridge classification of primes.

1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 2, 2, 4, 2, 3, 2, 3, 2, 1, 2, 3, 3, 1, 2, 2, 3, 1, 2, 2, 2, 2, 4, 2, 2, 2, 1, 4, 3, 4, 2, 2, 1, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 1, 3, 4, 2, 4, 2, 5, 2, 2, 3, 2, 3, 3, 2, 4, 3, 3, 5, 3, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 1, 2, 2, 2, 2, 4, 3, 4, 3, 1, 2, 4, 3, 3, 2, 3, 2, 2, 5, 3, 3, 2

Offset

1,5

Comments

This gives the "class-" number as opposed to the "class+" number. Not to be confused with the "class-number" of quadratic form theory.

a(n)=1 if A000040(n) is in A005109, a(n)=2 if A000040(n) is in A005110, a(n)=3 if A000040(n) is in A005111 etc.

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Index entries for sequences related to the Erdos-Selfridge classification

Formula

a(n) = max { a(p)+1 ; prime(p) is > 3 and divides prime(n)-1 } union { 1 } - M. F. Hasler, Apr 16 2007

Maple

A126805 := proc(n)
    option remember;
    local p, pe, a;
    if isprime(n) then
        a := 1;
        for pe in ifactors(n-1)[2] do
            p := op(1, pe);
            if p > 3 then
                a := max(a, procname(p)+1);
            end if;
        end do;
        a ;
    else
        -1;
    end if;
end proc:
seq(A126805(ithprime(n)), n=1..100) ;

Mathematica

a [n_] := a[n] = Module[{p, pf, e, res}, If[PrimeQ[n], pf = FactorInteger[n-1]; res = 1; For[e = 1, e <= Length[pf], e++, p = pf[[e, 1]]; If[p > 3, res = Max[res, a[p]+1]]]; Return[res], -1]]; Table[a[Prime[n]], {n, 1, 105}] (* Jean-François Alcover, Dec 13 2013, translated from Maple *)

Prog

(PARI) A126805(n) = { if( n>0, n=-prime(n)); if(( n=factor(-1-n)[, 1] ) & n[ #n]>3, vecsort( vector( #n, i, A126805(-n[i]) ))[ #n]+1, 1) } \\ M. F. Hasler, Apr 16 2007

Crossrefs

Cf. A056637.

Sequence in context: A127832 A107249 A062842 * A288003 A304382 A304717

Adjacent sequences: A126802 A126803 A126804 * A126806 A126807 A126808

Keyword

easy,nonn

Author

R. J. Mathar, Feb 23 2007

Status

approved