login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195268 Numbers whose sum of odd divisors is prime. 4
9, 18, 25, 36, 50, 72, 100, 144, 200, 288, 289, 400, 576, 578, 729, 800, 1152, 1156, 1458, 1600, 1681, 2304, 2312, 2401, 2916, 3200, 3362, 3481, 4608, 4624, 4802, 5041, 5832, 6400, 6724, 6962, 7921, 9216, 9248, 9604, 10082, 10201, 11664, 12800 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Odd numbers k^2 such that sigma(k^2) is prime, times an arbitrary power of two. - Charles R Greathouse IV, Sep 14 2011
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
The divisors of 2312 are { 1, 2, 4, 8, 17, 34, 68, 136, 289, 578, 1156, 2312 }, and the sum of the odd divisors 1 + 17 + 289 = 307 is prime. Hence 2312 = 2*34^2 is in the sequence.
MAPLE
with(numtheory):for n from 1 to 20000 do:x:=divisors(n):n1:=nops(x):s:=0:for m from 1 to n1 do:if irem(x[m], 2)=1 then s:=s+x[m]:fi:od:if type(s, prime)=true then printf(`%d, `, n): else fi:od:
MATHEMATICA
Select[Range[13000], PrimeQ[DivisorSigma[1, #/2^IntegerExponent[#, 2]]] &] (* Amiram Eldar, Jul 31 2022 *)
PROG
(PARI) list(lim)=my(v=List(), t); forstep(k=3, sqrt(lim), 2, if(isprime(sigma(t=k^2)), listput(v, t); while((t<<=1)<=lim, listput(v, t)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Sep 14 2011
CROSSREFS
Subsequence of A028982.
Sequence in context: A034046 A069562 A072502 * A371083 A328252 A227279
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 14 2011
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)