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A074985
Squares of semiprimes (A001358).
10
16, 36, 81, 100, 196, 225, 441, 484, 625, 676, 1089, 1156, 1225, 1444, 1521, 2116, 2401, 2601, 3025, 3249, 3364, 3844, 4225, 4761, 5476, 5929, 6724, 7225, 7396, 7569, 8281, 8649, 8836, 9025, 11236, 12321, 13225, 13924, 14161, 14641, 14884, 15129
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
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
Cf. A030514 (4th powers of primes), A085986 (squares of squarefree semiprimes).
Sequence in context: A125240 A050775 A022040 * A229134 A069262 A076956
KEYWORD
easy,nonn
AUTHOR
Jani Melik, Oct 07 2002
STATUS
approved