login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A280076 Numbers n such that Sum_{d|n} tau(d) = Product_{d|n} tau(d). 0
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 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=1..44.

FORMULA

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

EXAMPLE

9 is 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.

Sequence in context: A247078 A077438 A001248 * A052043 A188836 A030146

Adjacent sequences:  A280073 A280074 A280075 * A280077 A280078 A280079

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Dec 25 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 18:19 EDT 2018. Contains 316292 sequences. (Running on oeis4.)