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A093890 Number of primes arising as the sum of one or more divisors of n. 7
0, 2, 1, 4, 1, 5, 1, 6, 2, 7, 1, 9, 1, 5, 4, 11, 1, 12, 1, 13, 5, 5, 1, 17, 2, 5, 4, 16, 1, 20, 1, 18, 4, 6, 6, 24, 1, 5, 5, 24, 1, 24, 1, 18, 11, 5, 1, 30, 1, 15, 3, 18, 1, 30, 6, 30, 5, 7, 1, 39, 1, 3, 18, 31, 6, 34, 1, 16, 3, 34, 1, 44, 1, 4, 13, 16, 4, 39, 1, 42, 5, 5, 1, 48, 5, 5, 2, 41, 1, 51, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(2^n) = pi(2^(n+1)-1).

Except for n=3 and n=42, it appears that the records occur at the highly abundant numbers A002093. The record values appear to be pi(sigma(n)) for n in A002093, which means that these n are members of A093891. [T. D. Noe, Mar 19 2010]

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

EXAMPLE

a(4) = 4, the divisors of 4 are 1, 2 and 4.

Primes arising are 2, 3 = 1 + 2, 5 = 1 + 4 and 7 = 1 + 2 + 4.

MATHEMATICA

Do[l = Subsets[Divisors[n]]; l = Union[Map[Plus @@ #&, l]]; Print[Length[Select[l, PrimeQ]]], {n, 100}] (* Ryan Propper, Jun 04 2006 *)

CountPrimes[n_] := Module[{d=Divisors[n], t, lim, x}, t=CoefficientList[Product[1+x^i, {i, d}], x]; lim=PrimePi[Length[t]-1]; Count[t[[1+Prime[Range[lim]]]], _?(#>0 &)]]; Table[CountPrimes[n], {n, 100}] (* T. D. Noe, Mar 19 2010 *)

CROSSREFS

Cf. A093891, A093892.

Cf. A161510 (primes counted with repetition). [T. D. Noe, Mar 19 2010]

Sequence in context: A261242 A088296 A282738 * A325609 A006306 A322100

Adjacent sequences:  A093887 A093888 A093889 * A093891 A093892 A093893

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Apr 23 2004

EXTENSIONS

Corrected and extended by Ryan Propper, Jun 04 2006

STATUS

approved

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Last modified May 8 06:33 EDT 2021. Contains 343653 sequences. (Running on oeis4.)