A210934 - OEIS

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A210934

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

5

3, 4, 5, 6, 7, 9, 8, 9, 9, 10, 10, 21, 12, 15, 11, 11, 12, 33, 21, 12, 39, 13, 14, 13, 16, 22, 19, 13, 18, 24, 14, 18, 28, 16, 15, 25, 81, 45, 16, 34, 15, 22, 15, 99, 19, 16, 57, 17, 26, 30, 21, 16, 24, 17, 48, 20, 16, 25, 141, 52, 75, 19, 22, 22, 159, 58, 87

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OFFSET

1,1

COMMENTS

From an idea of Michael B. Porter.

LINKS

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

FORMULA

a(n) = A001414(A008864(n)). - Michel Marcus, Oct 05 2013

EXAMPLE

prime(8) = 19, and 19+1 = 20 = 2*2*5, so a(8) = 2+2+5 = 9.

MAPLE

A210934 := 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(A210934(n), n=1..300) ; # R. J. Mathar, May 25 2022

MATHEMATICA

A210934[n_] := Plus @@ Times @@@ FactorInteger[Prime[n] + 1];

Array[A210934, 100] (* Paolo Xausa, Sep 29 2025 *)

CROSSREFS

Cf. A001414, A008864, A023508, A023514, A210936

Sequence in context: A037350 A014615 A144046 * A354774 A194276 A184336

Adjacent sequences: A210931 A210932 A210933 * A210935 A210936 A210937

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Mar 30 2012

STATUS

approved