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 A060687 Numbers n such that there exist exactly 2 Abelian groups of order n, i.e., A000688(n) = 2. 28
 4, 9, 12, 18, 20, 25, 28, 44, 45, 49, 50, 52, 60, 63, 68, 75, 76, 84, 90, 92, 98, 99, 116, 117, 121, 124, 126, 132, 140, 147, 148, 150, 153, 156, 164, 169, 171, 172, 175, 188, 198, 204, 207, 212, 220, 228, 234, 236, 242, 244, 245, 260, 261, 268, 275, 276, 279 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS n belongs to this sequence iff exactly one prime in its factorization into prime powers has exponent 2 and all the other primes in the factorization have exponent 1, for example 60 = 2^2 * 3 * 5. Numbers n such that A046660(n) = 1. - Zak Seidov, Nov 14 2012 LINKS Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000 Eckford Cohen, Arithmetical notes. VIII. An asymptotic formula of Rényi, Proc. Amer. Math. Soc. 13 (1962), pp. 536-539. FORMULA n such that A001222(n)-A001221(n) = 1. Cohen proved that a(n) = kn + O(sqrt(n) log log n), where k = A013661/A179119 = 1/A271971 = 4.981178... - Charles R Greathouse IV, Aug 02 2016 MATHEMATICA Select[Range[500], PrimeOmega[#] - PrimeNu[#] == 1 &] (* Harvey P. Dale, Sep 08 2011 *) PROG (PARI) for(n=1, 279, if(bigomega(n)-omega(n)==1, print1(n, ", "))) (PARI) is(n)=factorback(factor(n)[, 2])==2 \\ Charles R Greathouse IV, Sep 18 2015 (PARI) list(lim)=my(s=lim\4, v=List(), u=vectorsmall(s, i, 1), t, x); forprime(k=2, sqrtint(s), t=k^2; forstep(i=t, s, t, u[i]=0)); forprime(k=2, sqrtint(lim\1), t=k^2; for(i=1, #u, if(u[i] && gcd(k, i)==1, x=t*i; if(x>lim, break); listput(v, x)))); Set(v) \\ Charles R Greathouse IV, Aug 02 2016 (Haskell) a060687 n = a060687_list !! (n-1) a060687_list = filter ((== 1) . a046660) [1..] -- Reinhard Zumkeller, Nov 29 2015 CROSSREFS Cf. A000688, A046660, A271971, A013661, A179119. Sequence in context: A304365 A038109 A067259 * A286228 A312863 A312864 Adjacent sequences:  A060684 A060685 A060686 * A060688 A060689 A060690 KEYWORD nonn AUTHOR Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 19 2001 EXTENSIONS Corrected and extended by Vladeta Jovovic, Jul 05 2001 STATUS approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)