OFFSET
1,1
COMMENTS
EXAMPLE
In the sequel, p,q,r denote arbitrary odd primes.
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.
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).
The a(3) = 12 PWN of the form 2^3*p*q*r range from 1713592 to 173482552.
The a(4) = 18 PWN of the form 2^4*p*q*r range from 15126992 to 6587973136.
The a(5) = 41 PWN of the form 2^5*p*q*r range from 569494624 to 297512429728.
PROG
(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}
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
M. F. Hasler, Feb 18 2018
STATUS
approved