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A085986 Squares of the squarefree semiprimes (p^2*q^2). 39
36, 100, 196, 225, 441, 484, 676, 1089, 1156, 1225, 1444, 1521, 2116, 2601, 3025, 3249, 3364, 3844, 4225, 4761, 5476, 5929, 6724, 7225, 7396, 7569, 8281, 8649, 8836, 9025, 11236, 12321, 13225, 13924, 14161, 14884, 15129, 16641, 17689, 17956, 19881 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is a member of a family of sequences directly related to A025487. First terms and known sequences are listed below: 1, A000007; 2, A000040; 4, A001248; 6, A006881; 8, A030078; 12, A054753; 16, A030514; 24, A065036; 30, A007304; 32, A050997; 36, this sequence; 48, ?; 60, ?; 64, ?; ....

Subsequence of A077448. The numbers in A077448 but not in here are 1, the squares of A046386, the squares of A067885, etc. - R. J. Mathar, Sep 12 2008

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Index to sequences related to prime signature

FORMULA

a(n) = A006881(n)^2.

EXAMPLE

A006881 begins 6 10 14 15 ... so this sequence begins 36 100 196 225 ...

MATHEMATICA

f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 2}; Select[Range[20000], f] (* Vladimir Joseph Stephan Orlovsky, Aug 14 2009 *)

Select[Range[200], PrimeOmega[#]==2&&SquareFreeQ[#]&]^2 (* Harvey P. Dale, Mar 07 2013 *)

PROG

(PARI) list(lim)=my(v=List(), x=sqrtint(lim\=1), t); forprime(p=2, x\2, t=p; forprime(q=2, min(x\t, p-1), listput(v, (t*q)^2))); Set(v) \\ Charles R Greathouse IV, Sep 22 2015

(PARI) is(n)=factor(n)[, 2]==[2, 2]~ \\ Charles R Greathouse IV, Oct 19 2015

CROSSREFS

Subsequence of A036785 and of A077448.

Cf. A025487.

Sequence in context: A030627 A177492 A077448 * A027603 A250813 A268770

Adjacent sequences:  A085983 A085984 A085985 * A085987 A085988 A085989

KEYWORD

easy,nonn,changed

AUTHOR

Alford Arnold, Jul 06 2003

STATUS

approved

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Last modified May 22 17:35 EDT 2017. Contains 286882 sequences.