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

1,1

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.

Formula

If a(n)=u*v, u<v, u,v are distinct terms of A050376 "Fermi-Dirac primes", then A064380(a(n))=a(n)-u-v+1+Sum{i>=1}(-1)^(i-1)*floor(v/u^i).

Mathematica

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

Crossrefs

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

Sequence in context: A131181 A064176 A000379 * A065985 A233421 A060652

Adjacent sequences: A176522 A176523 A176524 * A176526 A176527 A176528

Keyword

nonn

Author

Vladimir Shevelev, Apr 19 2010, Apr 20 2010

Extensions

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

Status

approved