A173325 Numbers k such that sigma(tau(k)) equals the sum of distinct primes dividing k.

3, 10, 104, 105, 175, 245, 276, 343, 414, 484, 532, 798, 1190, 1430, 1776, 1862, 3105, 3174, 3712, 4394, 5049, 5054, 5104, 5994, 6256, 6360, 6975, 8125, 8480, 8625, 9472, 9648, 10600, 12408, 12789, 14310, 16544, 16625, 16728, 19908, 20295, 21056, 21708

Offset: 1

Author

Michel Lagneau, Feb 16 2010

Keywords

• nonn

Comments

sigma(tau(k)) = A000203(A000005(k)) = A062069(k).

From Robert Israel, Nov 07 2016: (Start)

If m is in A023194, sigma(m)^(m-1) is in the sequence.

If p and q are distinct primes, and r and s are distinct primes such that r+s = (p+1)(q+1), then r^(p-1)*s^(q-1) is in the sequence.

(End)

Examples

			k=3 with sigma(tau(3)) = sigma(2) = 3 = A008472(3).
k=10 with sigma(tau(10)) = sigma(4) = 7 = A008472(10).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000
• 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 (1921), 75-113.
• W. Sierpinski, Number Of Divisors And Their Sum

Crossrefs

Cf. A001222, A001414, A062069, A173320.

Programs

Maple

with(numtheory): for n from 1 to 100000 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 :

Formula

{k: A062069(k) = A008472(k)}.

Extensions

"sopf" uses replaced and examples disentangled by R. J. Mathar, Feb 24 2010