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

1,1

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)

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

Formula

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

Example

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

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 :

Crossrefs

Cf. A001222, A001414, A062069, A173320.

Sequence in context: A023372 A025541 A203903 * A233257 A261127 A083108

Adjacent sequences: A173322 A173323 A173324 * A173326 A173327 A173328

Keyword

nonn

Author

Michel Lagneau, Feb 16 2010

Extensions

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

Status

approved