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A270337 Composite numbers equal to the number of divisors of one of their powers. 2
9, 25, 28, 40, 45, 49, 81, 121, 153, 169, 225, 289, 325, 343, 361, 441, 529, 625, 640, 841, 961, 976, 1089, 1225, 1369, 1521, 1681, 1849, 2133, 2197, 2209, 2401, 2541, 2601, 2809, 3025, 3249, 3481, 3721, 4225, 4489, 4753, 4761, 4851, 5041, 5329, 5929, 6241, 6348, 6561, 6859, 6889 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Prime numbers are not considered since every prime p satisfies p = d(p^(p-1)), where d() represents the number of divisors.

In general, p^k = d((p^k)^((p^k-1)/k)) for any prime p and for any power k such that (p^k-1)/k is an integer.

LINKS

Table of n, a(n) for n=1..52.

Paolo P. Lava, First 50 terms with their powers

EXAMPLE

9 = d(9^4); 28 = d(28^3); 153 = d(153^8); etc.

MAPLE

with(numtheory): P:=proc(q) local a, k, n;

for n from 2 to q do if not isprime(n) then a:=tau(n); k:=0;

while a<n do k:=k+1; a:=tau(n^k); od; if n=a then print(n); fi; fi; od; end: P(10^6);

MATHEMATICA

nn = 2000; Select[Select[Range@ nn, CompositeQ], Function[k, (SelectFirst[k^Range[nn/2], DivisorSigma[0, #] == k &] /. n_ /; MissingQ@ n -> 0) > 0]] (* Michael De Vlieger, Mar 17 2016, Version 10.2 *)

CROSSREFS

Cf. A000005, A073049, A270389.

Sequence in context: A321874 A020252 A076486 * A339842 A068529 A096059

Adjacent sequences:  A270334 A270335 A270336 * A270338 A270339 A270340

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava, Mar 15 2016

STATUS

approved

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Last modified January 22 14:23 EST 2021. Contains 340362 sequences. (Running on oeis4.)