A137489 -id:A137489 - cp's OEIS frontend

A274363 Numbers n such that n and n+1 both have 26 divisors.

689278976, 38492803071, 100821266432, 147331919871, 421606494207, 560920563711, 732088143872, 753855967232, 918212890624, 1218308829183, 1414219239423, 1485254832128, 1544826179583, 1566594002943, 1671079555071, 1675433119743, 1681165242368

Offset: 1

Charles R Greathouse IV, Jun 19 2016

nonn

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

Intersection of A005237 and A137489.

PARI
```
is(n)=numdiv(n)==26 && numdiv(n+1)==26
```

has(n)=if(n%4==2,ispower(n/2,12,&n) && isprime(n), bitand(n,8191)==4096 && isprime(n>>12) && n>8192) \\ check if n is even with 26 divisors
list(lim)=my(v=List(),t); forprime(p=2,sqrtnint(lim\=1,25), t=p^25; if(has(t+1), listput(v,t)); if(has(t-1), listput(v,t-1))); forprime(p=3,sqrtnint(lim\3,12), my(p12=p^12); forprime(q=3,lim\p12, if(p==q,next); t=p12*q; if(has(t+1), listput(v,t)); if(has(t-1), listput(v,t-1)))); Set(v)

A065985 Numbers k such that d(k) / 2 is prime, where d(k) = number of divisors of k.

Original entry on oeis.org

6, 8, 10, 12, 14, 15, 18, 20, 21, 22, 26, 27, 28, 32, 33, 34, 35, 38, 39, 44, 45, 46, 48, 50, 51, 52, 55, 57, 58, 62, 63, 65, 68, 69, 74, 75, 76, 77, 80, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 106, 111, 112, 115, 116, 117, 118, 119, 122, 123, 124, 125, 129, 133, 134

Offset: 1

Joseph L. Pe, Dec 10 2001

nonn

Numbers whose sorted prime signature (A118914) is either of the form {2*p-1} or {1, p-1}, where p is a prime. Equivalently, disjoint union of numbers of the form q^(2*p-1) where p and q are primes, and numbers of the form r * q^(p-1), where p, q and r are primes and r != q. - Amiram Eldar, Sep 09 2024

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000005, A118914.
Numbers with exactly 2*p divisors: A030513 (p=2), A030515 (p=3), A030628 \ {1} (p=5), A030632 (p=7), A137485 (p=11), A137489 (p=13), A175744 (p=17), A175747 (p=19).
Subsequences: A006881, A030078, A050997, A054753, A095990, A096156, A138031, A178739, A179665, A189987.

Select[Range[1, 1000], PrimeQ[DivisorSigma[0, # ] / 2] == True &]

n=0; for (m=1, 10^9, f=numdiv(m)/2; if (frac(f)==0 && isprime(f), write("b065985.txt", n++, " ", m); if (n==1000, return))) \\ Harry J. Smith, Nov 05 2009

is(n)=n=numdiv(n)/2; denominator(n)==1 && isprime(n) \\ Charles R Greathouse IV, Oct 15 2015

cp's OEIS Frontend

A274363 Numbers n such that n and n+1 both have 26 divisors.

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A065985 Numbers k such that d(k) / 2 is prime, where d(k) = number of divisors of k.

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