A101253 -id:A101253 - cp's OEIS frontend

A098661 a(n) = sum[i=1,n](i-th prime of Erdős-Selfridge classification i+). Cumulative sums of A101253.

2, 21, 134, 751, 2628, 11381, 63898, 318941, 1851114, 11138635, 59638094, 413291157, 2550007678, 20721795665, 132517178106

Offset: 1

Jonathan Vos Post, Dec 19 2004

nonn

The cumulative sums of the diagonalization of the set of sequences {j-th prime of Erdős-Selfridge classification k+}. The diagonalization itself is in A101253. a(1) = 2 and a(4) = 751 are primes. a(2) = 21 = 3 * 7, a(3) = 134 = 2 * 67; and a(6) = 11381 = 19 * 599 are semiprime. There are only 2 distinct digits in the greatest factor of a(10) = 11138635 = 5 * 2227727. The cumulative sums of the diagonalization of the related set of sequences {j-th prime of Erdős-Selfridge classification k-} is A101254. That n- diagonalization itself is in A101231.

			a(11) = 59638094 = 2 * 29 * 1028243 = 2+19+113+617+1877+8753+52517+255043+1532173+9287521+48499459

Cf. A101253, A101254, A101231.

More terms from David Wasserman, Mar 26 2008

A126433 Class+ number of prime(n) according to the Erdős-Selfridge classification of primes.

Original entry on oeis.org

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

Offset: 1

R. J. Mathar, Mar 23 2007

nonn

a(n)=1 if A000040(n) is in A005105. a(n)=2 if A000040(n) is in A005106, a(n)=3 if in A005107 etc. The locations of records are implicit in A005113.

Cf. A101253.

A126433 := proc(n)
    option remember;
    local p, pf, e, a;
    if isprime(n) then
        pf := ifactors(n+1)[2];
        a := 1;
        for e from 1 to nops(pf) do
            p := op(1, op(e, pf));
            if p > 3 then
                a := max(a, procname(p)+1);
            end if;
        end do;
        a ;
    else
        -1;
    end if;
end proc:
seq(A126433(ithprime(n)),n=1..100) ;
A126433 := n -> if n>0 then A126433(-ithprime(n)) else numtheory[factorset](1-n); if % subset{2,3} then 1 else 1+max(seq(A126433(-i),i=%)) fi fi; map(%,[$1..999]); # M. F. Hasler, Apr 02 2007

classPlus[p_] := classPlus[p] = If[f = FactorInteger[p + 1][[All, 1]]; q = Last[f]; q == 2 || q == 3, 1, Max[classPlus /@ f] + 1]; classPlus /@ Prime /@ Range[105] (* Jean-François Alcover, Jun 24 2013 *)

A126433(n) = { if( n>0, n=-prime(n)); n=factor(1-n)[,1]; if( n[ #n]>3, vecsort( vector( #n, i, A126433(-n[i]) ))[ #n]+1, 1) }; vector(999,i,A126433(i))

cp's OEIS Frontend

A098661 a(n) = sum[i=1,n](i-th prime of Erdős-Selfridge classification i+). Cumulative sums of A101253.

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A126433 Class+ number of prime(n) according to the Erdős-Selfridge classification of primes.

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