A098896 p(n)-adic valuation of the n-th superior highly composite number N(n), where p(n) = N(n)/N(n-1).

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, 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, 1, 1, 2, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

David Terr, Oct 14 2004

Keywords

• nonn

Comments

(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.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using the b-file at A000705)
• S. Ramanujan, Highly Composite Numbers.
• S. Ramanujan, Highly composite numbers, 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.

Crossrefs

Cf. A000705, A002201.

Extensions

More terms from Amiram Eldar, Aug 12 2019