A245202 Numbers k such that tau(k) + phi(k) is a perfect square.

3, 9, 21, 24, 26, 30, 51, 72, 77, 84, 90, 93, 100, 119, 122, 162, 168, 174, 194, 210, 213, 221, 276, 282, 291, 301, 381, 384, 386, 408, 414, 437, 469, 510, 527, 533, 564, 594, 597, 616, 723, 731, 744, 770, 791, 794, 858, 869, 896, 917, 930, 948, 952, 954

Offset

1,1

Comments

Numbers k such that A000010(k) + A000005(k) is a perfect square.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Chai Wah Wu)

Example

3 is in the sequence because phi(3) + tau(3) = 2 + 2 = 4^2.
9 is in the sequence because phi(9) + tau(9) = 6 + 3 = 3^2.
15 is not in the sequence because phi(15) + tau(15) = 8 + 4 = 12 = 2^2 * 3, which is not a perfect square.

Mathematica

Select[Range[1000], IntegerQ[Sqrt[DivisorSigma[0, #] + EulerPhi[#]]] &] (* Amiram Eldar, Apr 27 2024 *)

Prog

(PARI) isok(n) = issquare(numdiv(n) + eulerphi(n)); \\ Michel Marcus, Jul 23 2014
(Python)
from sympy import totient, divisor_count
from gmpy2 import is_square
[n for n in range(1, 10**4) if is_square(int(divisor_count(n)+totient(n)))] # Chai Wah Wu, Aug 04 2014

Crossrefs

Cf. A000005, A000010.

Sequence in context: A032668 A050839 A032640 * A127174 A251535 A191177

Adjacent sequences: A245199 A245200 A245201 * A245203 A245204 A245205

Keyword

nonn

Author

Reinhard Muehlfeld, Jul 13 2014

Status

approved