

A258883


Primitive weird numbers (PWN) of the form 2^k*p*q*r with k > 0 and where p < q < r are odd primes.


14



4030, 5830, 45356, 91388, 243892, 254012, 338572, 343876, 388076, 1713592, 8812312, 9928792, 11339816, 11547352, 15126992, 17999992, 29581424, 38546576, 74899952, 85389368, 89283592, 95327216, 141659096, 146764264, 162079768, 173482552, 569494624, 632874016
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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
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


LINKS



EXAMPLE

a(1) = 4030 = 2*5*13*31.
a(2) = 5830 = 2*5*11*53.
a(3) = 45356 = 2^2*17*23*29.


MATHEMATICA

(* 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 *)


PROG

(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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



