A210936 Sum of prime factors of prime(n)-1 (counted with multiplicity).

0, 2, 4, 5, 7, 7, 8, 8, 13, 11, 10, 10, 11, 12, 25, 17, 31, 12, 16, 14, 12, 18, 43, 17, 13, 14, 22, 55, 13, 15, 15, 20, 23, 28, 41, 15, 20, 14, 85, 47, 91, 15, 26, 15, 18, 19, 17, 42, 115, 26, 35, 26, 16, 17, 16, 133, 71, 16, 30, 18, 52, 77, 25, 38, 22, 83

Offset

1,2

Comments

From an idea of Michael B. Porter.

Let k = A003306(m) and p = 2*3^k + 1. Then for all n > pi(p), a(n) > a(pi(p)) = 3k + 2. For example, with k = 17, a(n) > a(14107188) = 53 for all n > 14107188. - Charles R Greathouse IV, Sep 29 2025

Links

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Formula

a(n) = A001414(A006093(n)). - Michel Marcus, Oct 05 2013

Example

prime(10) = 29, and 29-1 = 28 = 2*2*7, so a(10) = 2+2+7 = 11.

Maple

A210936 := proc(n)
        local p, pplus, f ;
        p := ithprime(n) ;
        pplus := ifactors(p-1)[2] ;
        add(op(1, f)*op(2, f), f=pplus) ;
end proc:
seq(A210936(n), n=1..300) ; # R. J. Mathar, May 25 2022

Mathematica

A210936[n_] := If[n == 1, 0, Plus @@ Times @@@ FactorInteger[Prime[n] - 1]];
Array[A210936, 100] (* Paolo Xausa, Sep 29 2025 *)

Prog

(PARI) a(n, p=prime(n))=my(f=factor(p-1)); f[, 1]~*f[, 2] \\ Charles R Greathouse IV, Sep 29 2025

Crossrefs

Cf. A001414, A006093, A023508, A023514, A210934, A003306.

Sequence in context: A224367 A308219 A288758 * A140203 A085888 A329531

Adjacent sequences: A210933 A210934 A210935 * A210937 A210938 A210939

Keyword

nonn

Author

Paolo P. Lava, Mar 30 2012

Status

approved