A280076 Numbers n such that Sum_{d|n} tau(d) = Product_{d|n} tau(d).

1, 4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 26569, 27889, 29929, 32041, 32761, 36481

Offset

1,2

Comments

Union of 1 and A001248 (squares of primes).

Numbers n such that A007425(n) = A211776(n).

Numbers n such that A007425(n) = Sum_{d|n} tau(d) = A211776(n) = Product_{d|n} tau(d) = 6.

Also squares of noncomposite numbers (A008578).

Subsequence of A350343. - Lorenzo Sauras Altuzarra, Sep 18 2022

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Formula

A007425(a(n)) = A211776(a(n)) = 6.

Apparently, a(n) = A331294(n + 3) if n > 5. - Lorenzo Sauras Altuzarra, Sep 18 2022

Example

9 is a term because Sum_{d|9} tau(d) = 1+2+3 = Product_{d|9} tau(d) = 1*2*3 = 6.

Mathematica

Select[Range@ 37500, Total@ # == Times @@ # &@ Map[DivisorSigma[0, #] &, Divisors@ #] &] (* Michael De Vlieger, Dec 25 2016 *)

Prog

(Magma) [n: n in [1..1000000] | &*[NumberOfDivisors(d): d in Divisors(n)]  eq &+[NumberOfDivisors(d): d in Divisors(n)]];
(PARI) isok(n) = my(d = divisors(n), nd = apply(numdiv, d)); vecsum(nd) == prod(k=1, #nd, nd[k]); \\ Michel Marcus, Jun 26 2017

Crossrefs

Cf. A001248, A007425, A008578, A211776, A331294, A350343.

Sequence in context: A077438 A350343 A001248 * A359757 A052043 A188836

Adjacent sequences: A280073 A280074 A280075 * A280077 A280078 A280079

Keyword

nonn

Author

Jaroslav Krizek, Dec 25 2016

Status

approved