A153357 Numbers n such that the harmonic number numerator A001008(n) is a semiprime.

4, 6, 11, 14, 15, 17, 19, 20, 23, 25, 31, 33, 34, 35, 37, 39, 49, 53, 55, 59, 61, 68, 90, 93, 94, 101, 116, 117, 121, 124, 145, 155, 158, 163, 169, 170, 186, 193, 194, 199, 205, 211, 214, 245, 258, 259, 264, 267, 283, 311, 315, 328, 340, 347, 359, 365, 371, 385

Offset: 1

Author

Alexander Adamchuk, Dec 24 2008

Keywords

• hard
• nonn

Comments

414, 421, 425, 436, 451, 452, and 480 are in the sequence. 391 and 476 are the remaining candidates below 500. - Daniel M. Jensen, Jun 26 2020

Numerator(H_391) is fully factored and confirmed semiprime with the help of NFS@Home. - Tyler Busby, May 06 2024

References

• R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 259.
• G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, page 347.
• D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 1, p. 615

Links

• Tyler Busby, Table of n, a(n) for n = 1..65
• FactorDB, Status of Numerator(H_476) in factordb.com
• Hisanori Mishima, Wolstenholme number (n = 1 to 100, n = 101 to 200, n = 201 to 300, n = 301 to 400, n = 401 to 500, n = 501 to 600).
• Eric Weisstein's World of Mathematics, Wolstenholme's Theorem, Harmonic Number.

Crossrefs

Cf. A001008 (numerators of harmonic number H(n)=Sum_{i=1..n} 1/i).

Cf. A002805, A056903, A067657.

Extensions

More terms from Sean A. Irvine, Aug 22 2011

Two missing terms added by D. S. McNeil, Aug 23 2011

More terms from Sean A. Irvine, Apr 01 2013

Two more terms from Daniel M. Jensen, Jun 26 2020