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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
M. F. Hasler, Table of n, a(n) for n = 1..121 (Using A002975(1..1073) calculated by Robert G. Wilson v.)
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
Sequence in context: A242864 A247689 A258401 * A352752 A249107 A329881
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified May 23 17:39 EDT 2024. Contains 372765 sequences. (Running on oeis4.)