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A156542

Number of distinct Sophie Germain prime factors of n.

0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 0, 1, 2, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 1, 1, 1, 2, 2, 1, 1, 2, 0, 3, 0, 1, 1, 1, 1, 3, 0, 1, 2, 2, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 3, 0, 2, 1, 1, 1, 2, 0, 1, 2, 2, 0, 2, 0, 1, 2

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OFFSET

1,6

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) <= A001221(n).

a(A156541(n)) = A001221(A156541(n)); a(A156543(n)) = 0.

a(A005384(n)) = 1; a(A053176(n)) = 0.

a(n) = Sum_{p|n} A101264(p), where p is a prime. - Ridouane Oudra, Aug 25 2019

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A005384(k) (see A005384 for an estimate of this sum). - Amiram Eldar, Jun 03 2024

MAPLE

with(numtheory): A101264:=p-> pi(2*p+1)-pi(2*p): seq(add(A101264(p), p in factorset(n)), n=1..100); # Ridouane Oudra, Aug 25 2019

MATHEMATICA

Join[{0}, Table[Count[FactorInteger[n][[All, 1]], _?(PrimeQ[2#+1]&)], {n, 2, 110}]] (* Harvey P. Dale, Apr 05 2020 *)

PROG

(Magma) [0] cat [&+[#PrimesInInterval(2*p, 2*p+1):p in PrimeDivisors(n)]:n in [2..100]]; // Marius A. Burtea, Aug 25 2019

CROSSREFS

Cf. A000720, A001221, A005384, A053176, A156541, A156543, A101264.

Sequence in context: A025911 A060184 A055639 * A307990 A066360 A061358

Adjacent sequences: A156539 A156540 A156541 * A156543 A156544 A156545

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 10 2009

STATUS

approved