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A195268
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Numbers whose sum of odd divisors is prime.
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4
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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
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OFFSET
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1,1
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COMMENTS
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Odd numbers k^2 such that sigma(k^2) is prime, times an arbitrary power of two. - Charles R Greathouse IV, Sep 14 2011
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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Select[Range[13000], PrimeQ[DivisorSigma[1, #/2^IntegerExponent[#, 2]]] &] (* Amiram Eldar, Jul 31 2022 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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