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A245202
Numbers k such that tau(k) + phi(k) is a perfect square.
1
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
Sequence in context: A032668 A050839 A032640 * A127174 A251535 A191177
KEYWORD
nonn
AUTHOR
Reinhard Muehlfeld, Jul 13 2014
STATUS
approved