cp's OEIS Frontend

A059992 Numbers with an increasing number of nonprime divisors.

%I A059992 #21 Jan 04 2025 22:38:51
%S A059992 1,4,8,12,24,36,48,60,72,120,180,240,360,720,840,1080,1260,1440,1680,
%T A059992 2160,2520,4320,5040,7560,10080,15120,20160,25200,27720,30240,45360,
%U A059992 50400,55440,75600,83160,110880,151200,166320,221760,277200,332640
%N A059992 Numbers with an increasing number of nonprime divisors.
%C A059992 Positions of records in A033273.
%C A059992 From _Michael De Vlieger_, Jan 04 2025: (Start)
%C A059992 Conjecture: This sequence includes all highly composite numbers (from A002182) except 2 and 6, but there are other terms in this sequence (e.g., a(3) = 8, a(9) = 72) that are not highly composite.
%C A059992 Conjecture: a(n)/A007947(a(n)) is in A301414. (End)
%H A059992 Amiram Eldar, <a href="/A059992/b059992.txt">Table of n, a(n) for n = 1..571</a> (terms 1..146 from Ray Chandler)
%H A059992 Michael De Vlieger, <a href="/A059992/a059992.png">Plot S(n) = P(omega(n))*m at (x,y) = (m, omega(n))</a>, where S is the union of A002182 and this sequence, P is A002110, omega is A001221, and only select m that harbor S(n) shown. Shows the coincidence of many terms in this sequence with A002182. Blue represents m in A002182, gold m in both A002182 and this sequence; dark blue represents m in A002201 (and also in A002182), orange m in both A002201 and this sequence; red indicates terms in this sequence that are not in A002182. Green highlights terms in A002182 but are not determined to be in this sequence.
%e A059992 a(4)=12 because twelve has 4 nonprime divisors {1, 4, 6 and 12} whereas a(3)=8 has only 3; and twelve is the first number greater than eight which exhibits this property.
%t A059992 l = 0; Do[ c = Count[PrimeQ[ Divisors[n] ], False]; If[c > l, l = c; Print[n] ], {n, 1, 10^6} ]
%o A059992 (PARI) lista(nn) = {my(m=0, nb); for (n=1, nn, nb = sumdiv(n, d, !isprime(d)); if (nb > m, m = nb; print1(n, ", ")););} \\ _Michel Marcus_, Jul 16 2019
%Y A059992 Cf. A055079, A002182, A033273, A180040.
%K A059992 nonn
%O A059992 1,2
%A A059992 _Robert G. Wilson v_, Mar 08 2001
%E A059992 Alternate description and b-file from _Ray Chandler_, Aug 07 2010