A175747 -id:A175747 - cp's OEIS frontend

A175749 Numbers with 40 divisors.

1680, 2160, 2640, 3024, 3120, 3240, 3696, 4080, 4368, 4536, 4560, 4752, 5520, 5616, 5670, 5712, 6000, 6160, 6384, 6864, 6960, 7128, 7280, 7344, 7440, 7680, 7728, 8208, 8424, 8880, 8910, 8976, 9520, 9744, 9840, 9936, 10032, 10320, 10368, 10416, 10530, 10608

Offset: 1

Jaroslav Krizek, Aug 27 2010

nonn

Numbers of the forms p^39, p^19*q^1, p^9*q^3, p^7*q^4, p^9*q^1*r^1, p^4*q^3*r^1 (A179698), and p^4*q^1*r^1*s^1 (A179693), where p, q, r, and s are distinct primes.

T. D. Noe, Table of n, a(n) for n = 1..1000
OEIS Wiki, Index entries for number of divisors

Cf. A175747, A175748.

Select[Range[20000],DivisorSigma[0,#]==40&] (* Vladimir Joseph Stephan Orlovsky, May 06 2011 *)

is(n)=numdiv(n)==40 \\ Charles R Greathouse IV, Jun 19 2016

A000005(a(n))=40.

A175748 Numbers with 39 divisors.

Original entry on oeis.org

36864, 102400, 200704, 495616, 692224, 1183744, 1478656, 2125764, 2166784, 3444736, 3936256, 5607424, 6885376, 7573504, 9048064, 11505664, 13286025, 14258176, 15241216, 18386944, 20647936, 21827584, 25563136, 26040609, 28217344, 32444416, 38539264, 41783296

Offset: 1

Jaroslav Krizek, Aug 27 2010

nonn

Numbers of the forms p^38 and p^12*q^2, where p and q are distinct primes.

T. D. Noe, Table of n, a(n) for n = 1..1000
OEIS Wiki, Index entries for number of divisors

Cf. A000005, A139572, A175747.

Select[Range[7000000],DivisorSigma[0,#]==39&] (* Vladimir Joseph Stephan Orlovsky, May 06 2011 *)

is(n)=numdiv(n)==39 \\ Charles R Greathouse IV, Jun 19 2016

A000005(a(n)) = 39.

Sum_{n>=1} 1/a(n) = P(2)*P(12) - P(14) + P(38) = 0.0000500204..., where P is the prime zeta function. - Amiram Eldar, Jul 03 2022

Extended by T. D. Noe, May 08 2011

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

A274810 Numbers n such that n and n+1 both have 38 divisors.

Original entry on oeis.org

9399153082499072, 20164508489351168, 21992587709382656, 25039386409435136, 25537472011436031, 26756191491457023, 45443223518445567, 47474422651813887, 59772891590033408, 64241529683443712, 73381925783601152

Offset: 1

Charles R Greathouse IV, Jul 08 2016

nonn

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

Intersection of A005237 and A175747.

PARI
```
is(n)=numdiv(n)==38 && numdiv(n+1)==38
```

has(n)=if(n%4==2, ispower(n/2, 18, &n) && isprime(n), bitand(n, 524287)==262144 && isprime(n>>18) && n>262144) \\ check if n is even with 38 divisors
list(lim)=my(v=List(), t); forprime(p=2, sqrtnint(lim\=1, 37), t=p^37; if(has(t+1), listput(v, t)); if(has(t-1), listput(v, t-1))); forprime(p=3, sqrtnint(lim\3, 18), my(p18=p^18); forprime(q=3, lim\p18, if(p==q, next); t=p18*q; if(has(t+1), listput(v, t)); if(has(t-1), listput(v, t-1)))); Set(v)

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A175749 Numbers with 40 divisors.

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A175748 Numbers with 39 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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A274810 Numbers n such that n and n+1 both have 38 divisors.

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PARI