%I #33 Nov 15 2017 04:30:14
%S 4030,5830,45356,91388,243892,254012,338572,343876,388076,1713592,
%T 8812312,9928792,11339816,11547352,15126992,17999992,29581424,
%U 38546576,74899952,85389368,89283592,95327216,141659096,146764264,162079768,173482552,569494624,632874016
%N Primitive weird numbers (PWN) of the form 2^k*p*q*r with k > 0 and where p < q < r are odd primes.
%C The condition k > 0 is not really a limitation since a product of three odd primes cannot be weird. -- Numbers of the form 2^k*p^2*q having only two distinct odd prime divisors, e.g., A258401(45) = 2319548096 = 2^6 * 137^2 * 1931 or A258401(143) = 232374697216 = 2^8 * 797^2 * 1429, are neither in A258882 nor in the present sequence as it is currently defined, although they are in the set of weird numbers 2^k*p*q*r with odd primes p,q,r. (PWN with nonsquarefree odd part are listed in A273815.) - _M. F. Hasler_, Jul 18 2016, amended Nov 09 2017
%C It appears that there are (2, 7, 12, 18, 41, ...) terms with k = valuation(a(n),2) = 1, 2, 3, etc. The smallest and largest such are (4030, 45356, 1713592, 15126992, 569494624, 5353519168, 96743686016, 1009572479744, ...) resp. (5830, 388076, 173482552, 6587973136, 297512429728, ...). - _M. F. Hasler_, Nov 09 2017
%H M. F. Hasler, <a href="/A258883/b258883.txt">Table of n, a(n) for n = 1..121</a> (Using A002975(1..1073) calculated by _Robert G. Wilson v_.)
%e a(1) = 4030 = 2*5*13*31.
%e a(2) = 5830 = 2*5*11*53.
%e a(3) = 45356 = 2^2*17*23*29.
%t (* copy the terms from A002975, assign them to 'lst' and then *) Select[ lst, PrimeNu@# == 4 &] (* WARNING: this code selects PWN with 3 distinct odd prime factors but does not exclude that they occur with multiplicity > 1, which is forbidden by definition of this sequence. - _M. F. Hasler_, Jul 12 2016 *)
%o (PARI) select(w->factor(w)[,2][^1]~==[1,1,1], A002975) \\ Assuming that A002975 is defined as set or vector. - _M. F. Hasler_, Jul 12 2016
%Y Cf. A002975, A258401, A258882, A258884, A258885.
%K nonn
%O 1,1
%A _Douglas E. Iannucci_ and _Robert G. Wilson v_, Jun 14 2015