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A173582 Numbers k such that sigma(tau(k)) = rad(k). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A157086 A051376 A101721 * A065973 A110973 A136411

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

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Last modified January 26 10:40 EST 2020. Contains 331279 sequences. (Running on oeis4.)