A074985 Squares of semiprimes (A001358).

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

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

Cf. A001358, A085548, A085964.

Cf. A030514 (4th powers of primes), A085986 (squares of squarefree semiprimes).

Sequence in context: A125240 A050775 A022040 * A229134 A069262 A076956

Adjacent sequences: A074982 A074983 A074984 * A074986 A074987 A074988

Keyword

easy,nonn

Author

Jani Melik, Oct 07 2002

Status

approved