A176525 Fermi-Dirac semiprimes: products of two distinct terms of A050376.

6, 8, 10, 12, 14, 15, 18, 20, 21, 22, 26, 27, 28, 32, 33, 34, 35, 36, 38, 39, 44, 45, 46, 48, 50, 51, 52, 55, 57, 58, 62, 63, 64, 65, 68, 69, 74, 75, 76, 77, 80, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 100, 106, 111, 112, 115, 116, 117, 118, 119, 122

Offset: 1

Author

Vladimir Shevelev, Apr 19 2010, Apr 20 2010

Keywords

• nonn

Comments

The sequence essentially differs from A000379 beginning with a(108)=212 (not 210). All squarefree terms of A001358 are in the sequence.

References

• Vladimir S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences, Vol. 4 (1996), pp. 28-43 [Russian].

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..10000
• Simon Litsyn and Vladimir S. Shevelev, On factorization of integers with restrictions on the exponent, INTEGERS: Electronic Journal of Combinatorial Number Theory, Vol. 7 (2007), Article #A33, pp. 1-36.

Crossrefs

Cf. A001358, A050376, A000379, A176472, A176509, A064380, A050292.

Programs

Mathematica

Select[Range[120], Plus @@ DigitCount[Last /@ FactorInteger[#], 2, 1] == 2 &] (* Amiram Eldar, Nov 27 2020 *)

Formula

If a(n)=u*v, uA050376 "Fermi-Dirac primes", then A064380(a(n))=a(n)-u-v+1+Sum{i>=1}(-1)^(i-1)*floor(v/u^i).

Extensions

Effectively duplicate content (due to duplicate referenced sequence) removed by Peter Munn, Dec 19 2019