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A060687
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Numbers n such that there exist exactly 2 Abelian groups of order n, i.e., A000688(n) = 2.
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49
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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MATHEMATICA
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Select[Range[500], PrimeOmega[#] - PrimeNu[#] == 1 &] (* Harvey P. Dale, Sep 08 2011 *)
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PROG
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(PARI) for(n=1, 279, if(bigomega(n)-omega(n)==1, print1(n, ", ")))
(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..]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 19 2001
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EXTENSIONS
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STATUS
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approved
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