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A283549 Composite numbers n such that tau(n^(n-1)) is a prime. 1
4, 9, 16, 27, 49, 64, 121, 125, 169, 289, 1681, 1849, 2401, 3481, 4913, 5329, 11881, 12769, 16129, 18769, 24649, 29791, 32041, 32761, 38809, 39601, 44521, 63001, 69169, 76729, 78125, 79507, 85849, 96721, 124609, 130321, 134689, 143641, 167281, 175561, 187489, 237169, 316969, 326041, 332929, 380689, 383161, 434281, 491401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A proper subset of A280257 and of A025475.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..10556

MAPLE

with(numtheory): P:=proc(q) if not isprime(q) and isprime(tau(q^(q-1))) then q; fi; end:

seq(P(i), i=1..30000); # Paolo P. Lava, Mar 10 2017

MATHEMATICA

k = 1; lst = {}; While[k < 100001, If [ !PrimeQ@ k && PrimeQ[ DivisorSigma[0, k^(k -1)]], AppendTo[lst, k]]; k++]; lst (* or *)

mx = 10^6; Union@ Flatten@ Reap[ Do[ Sow@ Select[ Prime[ Range[ PrimePi[ mx^(1/e) ]]]^e, PrimeQ[1 + e (#-1)] &], {e, 2, Log2[mx]}]][[2, 1]] (* Giovanni Resta, Mar 10 2017 *)

PROG

(PARI) is(n)=!isprime(n) && ispseudoprime(numdiv(n^(n-1))) \\ Charles R Greathouse IV, Mar 10 2017

CROSSREFS

Cf. A280257, A025475.

Sequence in context: A301198 A009862 A132074 * A137354 A113495 A110997

Adjacent sequences:  A283546 A283547 A283548 * A283550 A283551 A283552

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Mar 10 2017

STATUS

approved

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Last modified August 1 08:54 EDT 2021. Contains 346385 sequences. (Running on oeis4.)