A153357 - OEIS

%I #30 Feb 16 2025 08:33:09

%S 4,6,11,14,15,17,19,20,23,25,31,33,34,35,37,39,49,53,55,59,61,68,90,

%T 93,94,101,116,117,121,124,145,155,158,163,169,170,186,193,194,199,

%U 205,211,214,245,258,259,264,267,283,311,315,328,340,347,359,365,371,385

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

%C 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

%C Numerator(H_391) is fully factored and confirmed semiprime with the help of NFS@Home. - _Tyler Busby_, May 06 2024

%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 259.

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, page 347.

%D D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 1, p. 615

%H Tyler Busby, <a href="/A153357/b153357.txt">Table of n, a(n) for n = 1..65</a>

%H FactorDB, <a href="http://factordb.com/index.php?id=1100000000452033740">Status of Numerator(H_476) in factordb.com</a>

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha126.htm">Wolstenholme number (n = 1 to 100</a>, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha127.htm">n = 101 to 200</a>, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha128.htm">n = 201 to 300</a>, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha1281.htm">n = 301 to 400</a>, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha1282.htm">n = 401 to 500</a>, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha1283.htm">n = 501 to 600)</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WolstenholmesTheorem.html">Wolstenholme's Theorem</a>, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>.

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

%Y Cf. A002805, A056903, A067657.

%K hard,nonn

%O 1,1

%A _Alexander Adamchuk_, Dec 24 2008

%E More terms from _Sean A. Irvine_, Aug 22 2011

%E Two missing terms added by _D. S. McNeil_, Aug 23 2011

%E More terms from _Sean A. Irvine_, Apr 01 2013

%E Two more terms from _Daniel M. Jensen_, Jun 26 2020