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A195332 Numbers such that the sum of the cube of the odd divisors is prime. 1
9, 18, 36, 72, 121, 144, 242, 288, 484, 576, 968, 1152, 1936, 2304, 3872, 4608, 7744, 9216, 15488, 18432, 30976, 36481, 36864, 61952, 72361, 72962, 73728, 123904, 144722, 145924, 146689, 147456, 247808, 259081, 289444, 291848, 293378, 294912 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is of the form m^2 or 2*m^2.

See the comments in A195268 (numbers such that the sum of the odd divisors is prime).

It is interesting to observe that the intersection of this sequence with A195268 gives {9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 9216, 18432, 36864, 73728, 146689, 147456, 293378, 294912,...} and contains the sequence A005010(n) (numbers of the form 9*2^n), but is not equal to this sequence. For example, up to n = 400000, the numbers 146689 and 293378 are not divisible by 9.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

The divisors of 18 are  { 1, 2, 3, 6, 9, 18}, and the sum of the cube of the odd divisors 1^3 + 3^3 + 9^3 =757 is prime. Hence 18 is in the sequence.

MAPLE

with(numtheory):for n from 1 to 400000 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]^3:fi:od:if type(s, prime)=true  then printf(`%d, `, n): else fi:od:

MATHEMATICA

  Module[{c=Range[800]^2, m}, m=Sort[Join[c, 2c]]; Select[m, PrimeQ[Total[ Select[ Divisors[#], OddQ]^3]]&]](* Harvey P. Dale, Jul 31 2012 *)

CROSSREFS

Cf. A005010, A066100 (sqrt of odd numbers here), A195268.

Sequence in context: A173942 A162689 A033896 * A005010 A245425 A000547

Adjacent sequences:  A195329 A195330 A195331 * A195333 A195334 A195335

KEYWORD

nonn

AUTHOR

Michel Lagneau, Sep 15 2011

STATUS

approved

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Last modified September 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)