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

%I

%S 2035980763136,218010592018431,413918027251712,921717810593792,

%T 957141387771903,1017635547447296,1119195504115712,1842969898713087,

%U 2057374251679743,2435402979278847,2913421405257728,3039120499474431,3129396016513023

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

%H Charles R Greathouse IV, <a href="/A274808/b274808.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) is(n)=numdiv(n)==34 && numdiv(n+1)==34

%o (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

%o 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)

%Y Intersection of A005237 and A175744.

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Jul 07 2016

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)