This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A280076 #21 Oct 25 2022 20:30:40 %S A280076 1,4,9,25,49,121,169,289,361,529,841,961,1369,1681,1849,2209,2809, %T A280076 3481,3721,4489,5041,5329,6241,6889,7921,9409,10201,10609,11449,11881, %U A280076 12769,16129,17161,18769,19321,22201,22801,24649,26569,27889,29929,32041,32761,36481 %N A280076 Numbers n such that Sum_{d|n} tau(d) = Product_{d|n} tau(d). %C A280076 Union of 1 and A001248 (squares of primes). %C A280076 Numbers n such that A007425(n) = A211776(n). %C A280076 Numbers n such that A007425(n) = Sum_{d|n} tau(d) = A211776(n) = Product_{d|n} tau(d) = 6. %C A280076 Also squares of noncomposite numbers (A008578). %C A280076 Subsequence of A350343. - _Lorenzo Sauras Altuzarra_, Sep 18 2022 %H A280076 Ray Chandler, <a href="/A280076/b280076.txt">Table of n, a(n) for n = 1..10000</a> %F A280076 A007425(a(n)) = A211776(a(n)) = 6. %F A280076 Apparently, a(n) = A331294(n + 3) if n > 5. - _Lorenzo Sauras Altuzarra_, Sep 18 2022 %e A280076 9 is a term because Sum_{d|9} tau(d) = 1+2+3 = Product_{d|9} tau(d) = 1*2*3 = 6. %t A280076 Select[Range@ 37500, Total@ # == Times @@ # &@ Map[DivisorSigma[0, #] &, Divisors@ #] &] (* _Michael De Vlieger_, Dec 25 2016 *) %o A280076 (Magma) [n: n in [1..1000000] | &*[NumberOfDivisors(d): d in Divisors(n)] eq &+[NumberOfDivisors(d): d in Divisors(n)]] %o A280076 (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 A280076 Cf. A001248, A007425, A008578, A211776, A331294, A350343. %K A280076 nonn %O A280076 1,2 %A A280076 _Jaroslav Krizek_, Dec 25 2016