cp's OEIS Frontend

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.

A068936 Numbers having the sum of distinct prime factors not greater than the sum of exponents in prime factorization, A008472(k) <= A001222(k).

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%I A068936 #29 May 15 2025 00:57:05
%S A068936 1,4,8,16,27,32,48,64,72,81,96,108,128,144,162,192,216,243,256,288,
%T A068936 320,324,384,432,486,512,576,640,648,729,768,800,864,972,1024,1152,
%U A068936 1280,1296,1458,1536,1600,1728,1792,1944,2000,2048,2187,2304,2560,2592,2916
%N A068936 Numbers having the sum of distinct prime factors not greater than the sum of exponents in prime factorization, A008472(k) <= A001222(k).
%C A068936 The product of any two terms is also a term. - _Amiram Eldar_, May 14 2025
%H A068936 Amiram Eldar, <a href="/A068936/b068936.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Reinhard Zumkeller)
%e A068936 a(5) = 27 = 3^3, 3 = 3.
%e A068936 a(10) = 81 = 3^4, 3 < 4.
%e A068936 a(100) = 16000 = 2^7 * 5^3,  2+5 < 7+3.
%e A068936 a(1000) = 10321920 = 2^15 * 3^2 * 5 * 7, 2+3+5+7 < 15+2+1+1.
%t A068936 fQ[n_] := Block[{f = FactorInteger@n}, Plus @@ Last /@ f >= Plus @@ First /@ f]; Select[ Range@3000, fQ@ # &] (* _Robert G. Wilson v_, Jan 16 2006 *)
%t A068936 Select[Range@ 3000, First@ Differences@ Map[Total, Transpose@ FactorInteger@ #] >= 0 &] (* _Michael De Vlieger_, Dec 08 2016 *)
%o A068936 (Haskell)
%o A068936 a068936 n = a068936_list !! (n-1)
%o A068936 a068936_list = [x | x <- [1..], a008472 x <= a001222 x]
%o A068936 -- _Reinhard Zumkeller_, Nov 10 2013
%o A068936 (PARI) isok(k) = {my(f = factor(k)); vecsum(f[,1]) <= bigomega(f);} \\ _Amiram Eldar_, May 14 2025
%Y A068936 Cf. A001222, A008472, A068935, A068937, A068938.
%Y A068936 Subsequences: A054411, A100716, A257278.
%K A068936 nonn
%O A068936 1,2
%A A068936 _Reinhard Zumkeller_, Mar 08 2002
%E A068936 More terms from _Robert G. Wilson v_, Jan 16 2006