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A009087 Numbers n such that the number of divisors of n is prime (i.e., numbers of the form p^(q-1) for primes p,q). 17
2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Invented by the HR Automatic Concept Formation Program. If the sum of divisors is prime, then the number of divisors is prime, i.e., this is a supersequence of A023194.

A010055(a(n)) * A010051(A100995(a(n))+1) = 1. - Reinhard Zumkeller, Jun 06 2013

REFERENCES

S. Colton, Automated Theory Formation in Pure Mathematics. New York: Springer (2002)

LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..12546 (terms 1..1000 from T. D. Noe)

S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.

FORMULA

p^(q-1), p, q primes.

EXAMPLE

tau(16)=5 and 5 is prime.

MATHEMATICA

Select[Range[250], PrimeQ[DivisorSigma[0, #]]&] (* Harvey P. Dale, Sep 28 2011 *)

PROG

(Haskell)

a009087 n = a009087_list !! (n-1)

a009087_list = filter ((== 1) . a010051 . (+ 1) . a100995) a000961_list

-- Reinhard Zumkeller, Jun 05 2013

(PARI) is(n)=isprime(isprimepower(n)+1) \\ Charles R Greathouse IV, Sep 16 2015

CROSSREFS

Subsequence of A000961.

Cf. A023194, A036454, A203967.

Sequence in context: A123193 A066724 A089237 * A026477 A079852 A084400

Adjacent sequences:  A009084 A009085 A009086 * A009088 A009089 A009090

KEYWORD

nice,nonn,easy

AUTHOR

Simon Colton (simonco(AT)cs.york.ac.uk)

STATUS

approved

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Last modified April 8 09:44 EDT 2020. Contains 333313 sequences. (Running on oeis4.)