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

Author

R. J. Mathar, Feb 23 2007

Keywords

• easy
• nonn

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

Crossrefs

Cf. A056637.

Programs

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 *)

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

Formula

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