A274808 Numbers n such that n and n+1 both have 34 divisors.

2035980763136, 218010592018431, 413918027251712, 921717810593792, 957141387771903, 1017635547447296, 1119195504115712, 1842969898713087, 2057374251679743, 2435402979278847, 2913421405257728, 3039120499474431, 3129396016513023

Offset: 1

Author

Charles R Greathouse IV, Jul 07 2016

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A005237 and A175744.

Programs

PARI

is(n)=numdiv(n)==34 && numdiv(n+1)==34

PARI

has(n)=if(n%4==2, ispower(n/2, 16, &n) && isprime(n), bitand(n, 131071)==65536 && isprime(n>>16) && n>65536) \\ check if n is even with 34 divisors
list(lim)=my(v=List(), t); forprime(p=2, sqrtnint(lim\=1, 33), t=p^33; if(has(t+1), listput(v, t)); if(has(t-1), listput(v, t-1))); forprime(p=3, sqrtnint(lim\3, 16), my(p16=p^16); forprime(q=3, lim\p16, if(p==q, next); t=p16*q; if(has(t+1), listput(v, t)); if(has(t-1), listput(v, t-1)))); Set(v)