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A173325
Numbers k such that sigma(tau(k)) equals the sum of distinct primes dividing k.
1
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 16 2010
EXTENSIONS
"sopf" uses replaced and examples disentangled by R. J. Mathar, Feb 24 2010
STATUS
approved