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%I #21 Oct 25 2022 20:30:40
%S 1,4,9,25,49,121,169,289,361,529,841,961,1369,1681,1849,2209,2809,
%T 3481,3721,4489,5041,5329,6241,6889,7921,9409,10201,10609,11449,11881,
%U 12769,16129,17161,18769,19321,22201,22801,24649,26569,27889,29929,32041,32761,36481
%N Numbers n such that Sum_{d|n} tau(d) = Product_{d|n} tau(d).
%C Union of 1 and A001248 (squares of primes).
%C Numbers n such that A007425(n) = A211776(n).
%C Numbers n such that A007425(n) = Sum_{d|n} tau(d) = A211776(n) = Product_{d|n} tau(d) = 6.
%C Also squares of noncomposite numbers (A008578).
%C Subsequence of A350343. - _Lorenzo Sauras Altuzarra_, Sep 18 2022
%H Ray Chandler, <a href="/A280076/b280076.txt">Table of n, a(n) for n = 1..10000</a>
%F A007425(a(n)) = A211776(a(n)) = 6.
%F Apparently, a(n) = A331294(n + 3) if n > 5. - _Lorenzo Sauras Altuzarra_, Sep 18 2022
%e 9 is a term because Sum_{d|9} tau(d) = 1+2+3 = Product_{d|9} tau(d) = 1*2*3 = 6.
%t Select[Range@ 37500, Total@ # == Times @@ # &@ Map[DivisorSigma[0, #] &, Divisors@ #] &] (* _Michael De Vlieger_, Dec 25 2016 *)
%o (Magma) [n: n in [1..1000000] | &*[NumberOfDivisors(d): d in Divisors(n)] eq &+[NumberOfDivisors(d): d in Divisors(n)]]
%o (PARI) isok(n) = my(d = divisors(n), nd = apply(numdiv, d)); vecsum(nd) == prod(k=1, #nd, nd[k]); \\ _Michel Marcus_, Jun 26 2017
%Y Cf. A001248, A007425, A008578, A211776, A331294, A350343.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Dec 25 2016
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