OFFSET
1,2
COMMENTS
It appears that the sequence {a(n)} consists entirely of squares. (This has been verified to a(431) = 998001 = 999^2.)
A number k appears in the sequence if and only if k is a square and floor(k/d(k)) is odd. This is because k mod d(k) = k - d(k) * floor(k/d(k)) and d(k) is odd if and only if k is square. [Hagen von Eitzen, Jun 12 2009]
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10000
EXAMPLE
k=4 has three divisors, so 4 mod d(4) = 1, which is odd. But 4 is even. Therefore 4 is a term of the sequence.
k=25 has three divisors, so 25 mod d(25) = 1, which is odd. 25 is also odd. Therefore 25 is not a term of the sequence.
MATHEMATICA
Select[Range[100]^2, OddQ@Quotient[#, DivisorSigma[0, #]] &] (* Ivan Neretin, Mar 23 2017 *)
PROG
(PARI) for(i=1, 999, k=i^2; if(floor(k/numdiv(k))%2, print1(k, ", "))) \\ Hagen von Eitzen, Jun 12 2009
(Python)
from sympy import divisor_count
print([n**2 for n in range(1, 1001) if int(math.floor(n**2/divisor_count(n**2)))%2]) # Indranil Ghosh, Mar 23 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Jun 11 2009
STATUS
approved