cp's OEIS Frontend

A273815 Primitive weird numbers (pwn) with nonsquarefree odd part.

%I A273815 #73 Jan 26 2020 14:53:32
%S A273815 1550860550,2319548096,66072609790,114141404156,232374697216
%N A273815 Primitive weird numbers (pwn) with nonsquarefree odd part.
%C A273815 Equivalently, primitive weird numbers (A002975) with at least one odd prime factor with multiplicity > 1. A subsequence of A258401.
%C A273815 Although some of them have only few prime divisors, these primitive weird numbers are not in the sequences A258882, A258883, A258884 defined to list "pwn of the form 2^k p*...*r with primes p<...<r" (=> squarefree). Sequence A258885 (pwn with 6 prime divisors) does not have this restriction. - _M. F. Hasler_, Jul 26 2016
%C A273815 a(6) <= 2^10*2081^2*129083 = 572417848896512, which is also in the sequence. - _M. F. Hasler_, Feb 15 2018
%H A273815 Gianluca Amato, Maximilian F. Hasler, Giuseppe Melfi, Maurizio Parton, <a href="https://doi.org/10.1016/j.jnt.2019.02.027">Primitive abundant and weird numbers with many prime factors</a>, Journal of Number Theory vol. 201 (2019) pp. 436-459. DOI: 10.1016/j.jnt.2019.02.027. (Preprint: arXiv:1802.07178.)
%e A273815 a(1) = 1550860550 = 2 * 5^2 * 29 * 37 * 137 * 211 = A258885(1): the smallest pwn with 6 (distinct) prime divisors.
%e A273815 a(2) = 2319548096 = 2^6 * 137^2 * 1931 = A258401(45), but not in A258882 nor A258883, cf. comment.
%e A273815 a(3) = 66072609790 = 2 * 5 * 11 * 127^2 * 167 * 223 = A258885(3).
%e A273815 a(4) = 114141404156 = 2^2 * 13^2 * 19 * 383 * 23203 = A258401(123), but not in A258884, cf. comment.
%e A273815 a(5) = 232374697216 = 2^8 * 797^2 * 1429 = A258401(143), but not in A258882 nor A258883, cf. comment.
%o A273815 (PARI) select(t->vecmax(factor(t)[,2][^1])>1, A002975) \\ Assuming that A002975 is defined as vector holding enough terms of that sequence
%Y A273815 Cf. A002975, A258401, A258882, A258883, A258884, A258885.
%K A273815 nonn,hard,more
%O A273815 1,1
%A A273815 _M. F. Hasler_, Jul 08 2016