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

1,2

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).

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.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000005, A000203, A007947, A062069.

Sequence in context: A366306 A051376 A101721 * A065973 A110973 A361195

Adjacent sequences: A173579 A173580 A173581 * A173583 A173584 A173585

Keyword

nonn

Author

Michel Lagneau, Feb 22 2010

Extensions

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

Status

approved