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A289385
Nonprime numbers k such that the sum of the divisors of k^2 is of the form m^2 + m + 1.
1
1, 4, 6, 22, 48, 64, 390, 429, 638, 682, 880, 2013, 2310, 2320, 2968, 2970, 3625, 4692, 5696, 5865, 7772, 9213, 9715, 9944, 10778, 11254, 12963, 13039, 13704, 15180, 23370, 27236, 27556, 34045, 34445, 36141, 44336, 53136, 54376, 58548, 73185, 78952, 105464
OFFSET
1,2
COMMENTS
The corresponding values of m are given by the sequence {0, 5, 9, 30, 81, 90, 718, 562, 900, 961, 1451, ...} containing the subsequence of perfect squares {0, 9, 81, 900, 961, 4624, 8100, ...}.
If k is prime, the sum of the divisors of k^2 is the trivial value k^2 + k + 1.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..500 (first 127 terms from Robert G. Wilson v)
EXAMPLE
22 is in the sequence because sigma(22^2) = 931 = 30^2 + 30 + 1.
MAPLE
with(numtheory):nn:=10^5:
for n from 1 to nn do:
if type(n, prime)=false
then
y:=sqrt(4*sigma(n^2)-3):
z :=(-1+y)/2:
if y=floor(y) and z=floor(z) then printf(`%d, `, n):
else
fi:fi:
od:
MATHEMATICA
fQ[n_] := ! PrimeQ@ n && Block[{sd = DivisorSigma[1, n^2]}, y = Sqrt[4sd -3]; z = (y -1)/2; y == Floor@ y && z == Floor@ z]; Select[Range@ 125491, fQ] (* Robert G. Wilson v, Jul 05 2017 *)
CROSSREFS
Sequence in context: A101143 A083157 A192154 * A151519 A061595 A062940
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 04 2017
STATUS
approved