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A153357
Numbers n such that the harmonic number numerator A001008(n) is a semiprime.
1
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
1,1
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
CROSSREFS
Cf. A001008 (numerators of harmonic number H(n)=Sum_{i=1..n} 1/i).
Sequence in context: A247336 A158138 A096833 * A310591 A002732 A144065
KEYWORD
hard,nonn
AUTHOR
Alexander Adamchuk, Dec 24 2008
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
STATUS
approved