A175050 -id:A175050 - cp's OEIS frontend

A175051 a(n) is the number of divisors of A175050(n).

1, 4, 4, 9, 9, 4, 8, 9, 16, 9, 9, 4, 9, 9, 9, 27, 16, 9, 9, 9, 25, 4, 9, 9, 27, 9, 8, 4, 27, 9, 16, 9, 9, 9, 16, 9, 9, 27, 9, 27, 4, 9, 9, 27, 27, 9, 9, 4, 9, 9, 9, 36, 9, 9, 9, 9, 16, 25, 27, 16, 27, 9, 27, 4, 9, 27, 27, 9, 9, 9, 9, 9, 9, 27, 16, 9, 9, 27, 9, 9, 9, 9, 9, 27, 9, 4, 9, 9, 9, 27, 64, 27

Offset: 1

Leroy Quet, Dec 08 2009

nonn

All terms of this sequence (as well as all of those of sequence A175050) are perfect powers. (I.e., the terms of both of these sequences are terms of sequence A001597.)

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A001597, A175050.

Block[{nn = 10^5, s}, s = Union@ Flatten@ Table[n^e, {e, Prime@ Range@ PrimePi@ Log2@ nn}, {n, nn^(1/e)}]; Select[DivisorSigma[0, s], MemberQ[s, #] &]] (* Michael De Vlieger, Nov 24 2017, after T. D. Noe at A001597 *)

Extended by Ray Chandler, Dec 10 2009

A175391 Perfect squares having a square number of divisors.

Original entry on oeis.org

1, 36, 100, 196, 225, 256, 441, 484, 676, 1089, 1156, 1225, 1296, 1444, 1521, 2116, 2601, 3025, 3249, 3364, 3844, 4225, 4761, 5476, 5929, 6561, 6724, 7225, 7396, 7569, 8281, 8649, 8836, 9025, 10000, 11236, 12321, 13225, 13924, 14161, 14884, 15129

Offset: 1

Leroy Quet, Apr 27 2010

nonn

From Robert Israel, Mar 20 2018: (Start)
If m and n are coprime members of the sequence, then m*n is in the sequence.
Includes all numbers of the forms p^(4*i*(i+1)) and p^(2*i)*q^(2*i) where p, q are distinct primes and i is a positive integer. (End)

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A063774, A175050. - Leroy Quet, May 16 2010

with(numtheory): a := proc (n) if type(sqrt(tau(n^2)), integer) = true then n^2 else end if end proc: seq(a(n), n = 1 .. 130); # Emeric Deutsch, May 11 2010

Select[Range[150], IntegerQ[Sqrt[DivisorSigma[0, #^2]]]&]^2 (* Vincenzo Librandi, Mar 21 2018 *)
Select[Range[150]^2,IntegerQ[Sqrt[DivisorSigma[0,#]]]&] (* Harvey P. Dale, Aug 16 2025 *)

isok(n) = issquare(n) && issquare(numdiv(n)); \\ Michel Marcus, Mar 21 2018

a(n) = A063774(n)^2. - Leroy Quet, May 16 2010

Extended by Emeric Deutsch and Jon E. Schoenfield, May 11 2010

A171755 Least positive integer k where k is a perfect power and the number of divisors of k = A001597(n).

Original entry on oeis.org

1, 8, 128, 36, 216, 1296, 900, 2147483648, 7776, 46656, 27000, 44100, 10077696, 60466176, 810000, 170141183460469231731687303715884105728, 362797056, 2176782336, 5832000, 24300000, 1587600, 2822400, 9261000, 2821109907456

Offset: 1

Ray Chandler, Dec 17 2009

nonn

a(n) is the least member of A001597 such that A000005(a(n)) = A001597(n).

Ray Chandler, Table of n, a(n) for n=1..113

Cf. A175050, A175051.

cp's OEIS Frontend

A175051 a(n) is the number of divisors of A175050(n).

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A175391 Perfect squares having a square number of divisors.

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A171755 Least positive integer k where k is a perfect power and the number of divisors of k = A001597(n).

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