The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #7 Nov 13 2024 17:17:56
%S 2,2,3,3,5,5,6,6,7,8,8,9,10,10,10,11,12,12,13,13,12,13,13,14,15,15,15,
%T 15,14,14,17,17,18,17,19,18,19,19,19,20,20,20,21,21,20,20,22,23,23,23,
%U 23,23,22,23,24,24,24,24,24,24,23,24,26,26,26,25,27,28,29
%N a(n) is the greatest number of prime factors with multiplicity of squarefree composite k such that k has lpf(k) = prime(n) such that m <= a(n), where lpf = A020639, m = floor(log k / log lpf(k)).
%C The smallest k such that lpf(k) = prime(n) with Omega(k) = A001222(k) = a(n) is the product of prime(n..n+a(n)-1).
%H Michael De Vlieger, <a href="/A377794/b377794.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael De Vlieger, <a href="/A377794/a377794.png">Log log scatterplot of a(n)</a>, n = 1..16384.
%e Table relating the first 12 terms with prime decomposition of smallest k in A377713 (or A377792) such that lpf(k) = prime(n) and Omega(k) = a(n):
%e n k prime factors of k a(n)
%e -----------------------------------------------------------------------
%e 1 6 2 * 3 2
%e 2 15 3 * 5 2
%e 3 385 5 * 7 * 11 3
%e 4 1001 7 * 11 * 13 3
%e 5 1062347 11 * 13 * 17 * 19 * 23 5
%e 6 2800733 13 * 17 * 19 * 23 * 29 5
%e 7 247110827 17 * 19 * 23 * 29 * 31 * 37 6
%e 8 595973171 19 * 23 * 29 * 31 * 37 * 41 6
%e 9 63392725189 23 * 29 * 31 * 37 * 41 * 43 * 47 7
%e 10 8618654420261 29 * 31 * 37 * 41 * 43 * 47 * 53 * 59 8
%e 11 18128893780549 31 * 37 * 41 * 43 * 47 * 53 * 59 * 61 8
%e 12 2781907990776503 37 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71 9
%t Table[j = 1; While[Times @@ Prime[Range[i + 1, i + j]] < Prime[i]^(j + 1), j++]; j, {i, 120}]
%Y Cf. A001222, A020639, A120944, A377713, A377792.
%K nonn,easy
%O 1,1
%A _Michael De Vlieger_, Nov 07 2024