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%I #12 Jul 04 2019 14:12:36
%S 2,7,12,18,41,130
%N Number of primitive weird numbers (PWN) of the form 2^n*p*q*r, where p,q,r are odd primes.
%C The analog of A258333 for three odd factors.
%C Note that this sequence counts PWN with nonsquarefree odd part, which are excluded from A258883, see also A273815.
%e In the sequel, p,q,r denote arbitrary odd primes.
%e The a(1) = 2 PWN of the form 2*p*q*r are A258883(1..2): 4030 = 2*5*13*31 and 5830 = 2*5*11*53.
%e The a(2) = 7 PWN of the form 2^2*p*q*r are 45356, 91388, 243892, 254012, 338572, 343876 and 388076, with (p,q,r) = (17, 23, 29), (11, 31, 67), (11, 23, 241), (11, 23, 251), (13, 17, 383), (13, 17, 389) and (13, 17, 439).
%e The a(3) = 12 PWN of the form 2^3*p*q*r range from 1713592 to 173482552.
%e The a(4) = 18 PWN of the form 2^4*p*q*r range from 15126992 to 6587973136.
%e The a(5) = 41 PWN of the form 2^5*p*q*r range from 569494624 to 297512429728.
%o (PARI) A299401(n,k=3,m=2^n,P=3,cnt=0,s)={if(k>1,forprime(p=P,,(s=sigma(m*p,-1))<2||next;p>P&&s*(1+1/p)^(k-1)<2&&break;/*printf("%d",[k,p]);*/cnt+=A299401(n,k-1,m*p,p)),s=sigma(m);my(p=1\(2*m/s-1)+1,d);while(P<p=precprime(p-1),/*print1([p]);*/is_A005835(m*p,d=divisors(m*p),s+(s-m)*p,#d-1)&&cnt++));cnt}
%Y Cf. A258883, A002975.
%K nonn,more,hard
%O 1,1
%A _M. F. Hasler_, Feb 18 2018
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