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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A292286 a(n) = k if the product of the divisors of n is n^k for some integer k, or -1 if no such k exists. For the ambiguous case, define a(1) = 0. 2
0, 1, 1, -1, 1, 2, 1, 2, -1, 2, 1, 3, 1, 2, 2, -1, 1, 3, 1, 3, 2, 2, 1, 4, -1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 2, -1, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 5, -1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 6, 1, 2, 3, -1, 2, 4, 1, 3, 2, 4, 1, 6, 1, 2, 3, 3, 2, 4, 1, 5, -1, 2, 1, 6, 2, 2, 2, 4, 1, 6, 2, 3, 2, 2, 2, 6, 1, 3, 3, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

If the number of divisors (nd) of n > 1 is odd, then a(n) = -1, else a(n) = nd/2. - Michel Marcus, Sep 14 2017

First occurrence of k beginning with -1 is A293570(r). - Robert G. Wilson v, Oct 10 2017

Records occur for A293570(r): 4, 6, 12, 24, 48, 60, 192, 240, 3072, 12288, 196608, 786432, 12582912, 805306368, etc. - Robert G. Wilson v, Oct 10 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(1) = 0, a(A000290(n+1)) = -1, a(A000037(n+1)) = A056924(A000037(n+1)), where A000290 = the squares and A000037 = the nonsquares.

EXAMPLE

a(10) = 2 because divisors of 10 are 1,2,5,10 with product 100 = 10^2.

MATHEMATICA

Table[Boole[n == 1] + If[OddQ@ #, -1, #/2] &@ DivisorSigma[0, n], {n, 100}] (* Michael De Vlieger, Sep 15 2017 *)

PROG

(PARI) a(n) = if (n==1, 0, my(nd = numdiv(n)); if (nd % 2, -1, nd/2)); \\ Michel Marcus, Sep 14 2017

(PARI) a(n)=my(k=numdiv(n)); if(k%2, if(n>1, -1, 0), k/2) \\ Charles R Greathouse IV, Sep 19 2017

CROSSREFS

Numbers n such that the product of divisors of n is n^k: A000040 (k = 1), A007422 (k = 2), A162947 (k = 3), A111398 (k = 4), A030628 (k = 5), A030630 (k = 6).

Cf. A000037, A000290, A056924, A007955, A293570.

Sequence in context: A087942 A320012 A241276 * A099042 A140774 A056924

Adjacent sequences:  A292283 A292284 A292285 * A292287 A292288 A292289

KEYWORD

sign

AUTHOR

Juri-Stepan Gerasimov, Sep 13 2017

EXTENSIONS

Definition corrected by Charles R Greathouse IV, Sep 13 2017

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 19 18:30 EST 2019. Contains 320327 sequences. (Running on oeis4.)