A069810 Integers k such that gcd(k, sigma(k)) = tau(k).

1, 56, 60, 96, 132, 184, 204, 248, 276, 348, 376, 480, 492, 504, 564, 568, 612, 632, 636, 708, 824, 852, 996, 1016, 1068, 1208, 1212, 1248, 1284, 1336, 1356, 1528, 1572, 1592, 1632, 1644, 1784, 1788, 1908, 1912, 1980, 2004, 2076, 2104, 2148, 2168, 2232

Offset: 1

Author

Benoit Cloitre, Apr 30 2002

Keywords

• easy
• nonn

Examples

			The divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, so tau(56) = 8 and sigma(56) = 120. As gcd(56, 120) = tau(56) = 8, so 56 belongs to this sequence. - _Bernard Schott_, Oct 18 2019
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A047727 (numbers that are arithmetic and refactorable).

Cf. A003601 (arithmetic numbers), A033950 (refactorable numbers).

Programs

Magma

[k:k in [1..2300]| Gcd(k,DivisorSigma(1,k)) eq #Divisors(k)]; // Marius A. Burtea, Oct 18 2019

Mathematica

Select[Range[2500], GCD[DivisorSigma[1, #], #] == DivisorSigma[0, #] &] (* Jayanta Basu, Mar 21 2013 *)

PARI

for(n=1,3000,if(gcd(n, sigma(n))==numdiv(n),print1(n,",")))