A173582 Numbers k such that sigma(tau(k)) = rad(k).

1, 3, 135, 336, 343, 375, 1134, 14406, 24336, 41067, 54756, 85293, 321408, 428544, 430080, 1028196, 1084752, 1651104, 1886976, 2476656, 2935296, 3066336, 3341637, 3577392, 4599504, 4881384, 5133375, 5366088, 5451264, 8347248, 8989344, 9240075, 9552816, 9871875

Offset: 1

Author

Michel Lagneau, Feb 22 2010

Keywords

• nonn

Comments

rad(k) is the product of the primes dividing k (A007947), tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisor of k (A000203).

Examples

			tau(3) = 2, sigma(2) = 3 and rad(3) = 3. tau(135) = 8, sigma(8) = 15 and rad(135) = 15. tau(14406) = 20, sigma(20) = 42 and rad(14406) = 42.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100
• C. K. Caldwell, The Prime Glossary, Number of divisors
• Wacław Sierpiński, Number Of Divisors And Their Sum, Elementary theory of numbers, Warszawa, 1964.

Crossrefs

Cf. A000005, A000203, A007947, A062069.

Programs

Maple

with(numtheory):for n from 1 to 1000000 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)):if sigma(tau(n)) = t2 then print (n): else fi : od :

Mathematica

Select[Range[500000], DivisorSigma[1, DivisorSigma[0, #]] == Times @@ (First@# & /@ FactorInteger[#]) &] (* Amiram Eldar, Jul 11 2019 *)

Formula

k such that A062069(k) = A007947(k).

Extensions

a(20)-a(34) from Donovan Johnson, Jan 14 2012