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A343732 Numbers k at which tau(k^k) is a prime power, where tau is the number-of-divisors function A000005. 0
2, 3, 4, 6, 7, 8, 9, 10, 15, 22, 26, 30, 31, 36, 42, 46, 58, 66, 70, 78, 82, 102, 106, 121, 127, 130, 138, 166, 178, 190, 210, 222, 226, 238, 255, 262, 282, 310, 330, 346, 358, 366, 382, 418, 430, 438, 441, 442, 462, 466, 478, 498, 502, 511, 546, 562, 570, 586 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

9^9 = (3^2)^9 = 3^18 has 19 = 19^1 divisors, so 9 is a term.

10^10 = 2^10 * 5^10 has 121 = 11^2 divisors, so 10 is a term.

11^11 has 12 = 2^2 * 3^1 divisors, so 11 is not a term.

MATHEMATICA

a={}; For[k=1, k<600, k++, If[PrimePowerQ[DivisorSigma[0, k^k]], AppendTo[a, k]]]; a (* Stefano Spezia, Jun 02 2021 *)

PROG

(PARI) isok(k) = isprimepower(numdiv(k^k)); \\ Michel Marcus, Jun 02 2021

(Python)

from functools import reduce

from operator import mul

from sympy import factorint

A343732_list = [n for n in range(2, 10**3) if len(factorint(reduce(mul, (n*d+1 for d in factorint(n).values())))) == 1] # Chai Wah Wu, Jun 03 2021

CROSSREFS

Cf. A000005, A000312, A062319, A246655.

Sequence in context: A226381 A180040 A166274 * A039168 A059589 A153287

Adjacent sequences:  A343729 A343730 A343731 * A343733 A343734 A343735

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Jun 01 2021

STATUS

approved

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Last modified September 21 06:57 EDT 2021. Contains 347596 sequences. (Running on oeis4.)