A173320 - OEIS

A173320

Numbers k such that tau(sigma(k)) = sopf(k).

2, 3, 4, 15, 16, 42, 45, 64, 81, 84, 245, 336, 340, 342, 460, 539, 550, 580, 605, 684, 882, 1012, 1014, 1160, 1344, 1360, 1640, 1674, 1700, 1785, 1840, 1972, 2178, 2254, 2320, 2322, 2736, 3096, 3348, 3645, 4048, 4096, 4212, 4332, 4389, 4400, 4644, 4830, 5022

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OFFSET

1,1

COMMENTS

sopf(k) is the sum of the distinct primes dividing k (A008472), tau(k) is the number of divisors of k (A000005), and sigma(k) is the sum of divisor of k (A000203).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

C. K. Caldwell, The Prime Glossary, Number of divisors

P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., 19 (1919), 75-113.

Wacław Sierpiński, Number Of Divisors And Their Sum, Elementary theory of numbers, Warszawa, 1964.

FORMULA

k such that A062068(k)= A008472(k).

EXAMPLE

sigma(2) = 3, tau(3) = 2 and sopf(2) = 2 sigma(2254) = 4104, tau(4104) = 32 and sopf(2254) = 32.

MAPLE

with(numtheory): for n from 1 to 12000 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)): if tau(sigma(n)) = t2 then print (n): else fi : od :

MATHEMATICA

Select[Range[2, 5100], DivisorSigma[0, DivisorSigma[1, #]]==Total[ FactorInteger[ #][[All, 1]]]&] (* Harvey P. Dale, May 31 2019 *)

CROSSREFS

Cf. A000005, A000203, A001414 (sopfr), A001222.

Sequence in context: A037323 A065812 A081350 * A135633 A269725 A270929

Adjacent sequences: A173317 A173318 A173319 * A173321 A173322 A173323

KEYWORD

nonn

AUTHOR

Michel Lagneau, Feb 16 2010

STATUS

approved