This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112779 #26 Feb 16 2025 08:32:59 %S A112779 0,1,2,1,2,3,2,4,2,3,2,4,3,4,3,2,4,3,4,3,5,4,6,4,3,4,5,4,3,5,4,6,4,5, %T A112779 4,5,6,4,3,5,4,6,4,5,4,5,6,4,6,7,5,4,4,6,4,5,4,5,6,4,6,7,5,4,4,6,5,5, %U A112779 4,6,5,6,4,6,7,5,4,6,5,7,6,5,6,4,4,6,7,5,5,4,6,6,5,7,6,5,6,4,7,6,7,5,7,6,8 %N A112779 Largest exponent in the prime factorization of highly composite numbers (definition 1, A002182). %C A112779 Each highly composite number can be written as the product of primorials (A002110); a(n) is also the number of primorials used in the product. %C A112779 a(i) is the exponent of 2 in the prime factorization of A002182(i), cf. formula. - _David A. Corneth_, Aug 16 2015; edited by _M. F. Hasler_, Jan 03 2020 %H A112779 T. D. Noe, <a href="/A112779/b112779.txt">Table of n, a(n) for n=1..10000</a> (using Flammenkamp's data) %H A112779 A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.txt">First 1200 highly composite numbers</a> %H A112779 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly Composite Number</a> %F A112779 a(n) = A007814(A002182(n)). - _David A. Corneth_, Aug 16 2015 %e A112779 A002182(8) = 48 = 2^4*3, which has largest exponent 4, so a(8)=4. %o A112779 (PARI) apply( A112779(n)=valuation(A002182(n),2), [1..99]) \\ _M. F. Hasler_, Jan 03 2020 %Y A112779 Cf. A002110, A002182, A002183, A007814, A108602, A112778, A112780, A112781. %K A112779 nonn %O A112779 1,3 %A A112779 _Ray Chandler_, Nov 11 2005