A098896 - OEIS

%I #14 Aug 13 2019 04:36:16

%S 1,1,2,1,3,2,1,4,1,1,5,3,2,1,1,6,1,2,1,4,1,7,1,1,1,1,3,1,1,8,2,1,5,1,

%T 1,1,1,2,1,1,9,1,1,1,1,3,1,1,2,1,1,1,1,6,4,1,1,2,10,1,1,1,1,1,1,1,1,1,

%U 1,1,2,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1

%N p(n)-adic valuation of the n-th superior highly composite number N(n), where p(n) = N(n)/N(n-1).

%C (1+1/a(n)) appears in the denominators of the log arguments of the denominators of the numbers in the table of the reference, pp. 115-117.

%H Amiram Eldar, <a href="/A098896/b098896.txt">Table of n, a(n) for n = 1..10000</a> (calculated using the b-file at A000705)

%H S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/Cpaper15/page1.htm">Highly Composite Numbers</a>.

%H S. Ramanujan, <a href="https://doi.org/10.1112/plms/s2_14.1.347">Highly composite numbers</a>, Proc. Lond. Math. Soc. 14 (1915), 347-409; reprinted in Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962, pp. 78-129. See esp. pp. 87, 115-117.

%e a(8) = 4 since N(8)=5040 has 2-adic valuation of 4 and N(8)/N(7)=2.

%Y Cf. A000705, A002201.

%K nonn

%O 1,3

%A _David Terr_, Oct 14 2004

%E More terms from _Amiram Eldar_, Aug 12 2019