OFFSET
1,1
COMMENTS
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., 19 (1919), 75-113.
EXAMPLE
4 is in the sequence: tau(4) = 3, tau(3) = 2; sopf(4) = 2, sopf(2) = 2.
546 is in the sequence: tau(546) = 16, tau(16) = 5; sopf(546) = 25, sopf(25) = 5.
MAPLE
with(numtheory): for n from 1 to 60000 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)): tt1:= ifactors(t2)[2] : tt2 :=sum(tt1[i][1], i=1..nops(tt1)):if tau(tau(n))= tt2 then print (n): else fi : od :
# second Maple program:
with(numtheory): sopf:= n-> add(i, i=factorset(n)):
a:= proc(n) option remember; local k;
for k from 1+ `if`(n=1, 0, a(n-1))
while tau(tau(k)) <> sopf(sopf(k)) do od; k
end:
seq(a(n), n=1..100); # Alois P. Heinz, Aug 26 2010
MATHEMATICA
Select[Range[4100], DivisorSigma[0, DivisorSigma[0, #]]==Total[ Transpose[ FactorInteger[ Total[Transpose[FactorInteger[#]][[1]]]]][[1]]]&] (* Harvey P. Dale, Aug 05 2013 *)
PROG
(Magma) f:=func<n|NumberOfDivisors(n)>; g:=func<n|&+PrimeDivisors(n)>; [k:k in [2..5000]|f(f(k)) eq g(g(k)) ]; // Marius A. Burtea, Nov 14 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 16 2010
EXTENSIONS
Corrected and edited by Michel Lagneau, Apr 25 2010
STATUS
approved