OFFSET
1,1
COMMENTS
Disjoint union of 4th powers of primes, A030514, and squares of squarefree semiprimes, A085986. - M. F. Hasler, Nov 12 2021
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ (n log n/log log n)^2. - Charles R Greathouse IV, Oct 16 2015
Sum_{n>=1} 1/a(n) = (P(2)^2 + P(4))/2 = (A085548^2 + A085964)/2 = 0.1407604343..., where P is the prime zeta function. - Amiram Eldar, Oct 30 2020
EXAMPLE
4 is divisible by 2 (twice) and 4*4 = 16.
6 is divisible by exactly 2 and 3 and 6*6 = 36.
MAPLE
readlib(issqr): ts_kv_sp := proc(n); if (numtheory[bigomega](n)=4 and issqr(n)='true') then RETURN(n); fi; end: seq(ts_kv_sp(i), i=1..50000);
MATHEMATICA
Select[Range[200], PrimeOmega[#]==2&]^2 (* Harvey P. Dale, Oct 03 2011 *)
PROG
(Haskell)
a074985 = a000290 . a001358 -- Reinhard Zumkeller, Aug 02 2012
(PARI) is(n)=if(issquare(n, &n), isprimepower(n)==2 || factor(n)[, 2]==[1, 1]~, 0) \\ Charles R Greathouse IV, Oct 16 2015
(PARI) list(lim)=lim=sqrtint(lim\1); my(v=List()); forprime(p=2, sqrtint(lim), forprime(q=p, lim\p, listput(v, (p*q)^2))); Set(v) \\ Charles R Greathouse IV, Nov 13 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jani Melik, Oct 07 2002
STATUS
approved