A175750 -id:A175750 - cp's OEIS frontend

A175756 Numbers with 50 divisors.

6480, 9072, 14256, 16848, 22032, 24624, 29808, 30000, 37584, 40176, 41472, 47952, 53136, 55728, 60912, 68688, 70000, 76464, 79056, 86832, 92016, 94608, 101250, 102384, 107568, 110000, 115248, 115344, 125712, 130000, 130896, 133488

Offset: 1

Jaroslav Krizek, Aug 27 2010

nonn

Numbers of the forms p^49, p^24*q^1, p^9*q^4 and p^4*q^4*r^1 (A190012), where p, q and r are distinct primes.

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

Cf. A137484, A137488, A175750.

Select[Range[200000], DivisorSigma[0, #] == 50 &] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *)

is(n)=numdiv(n)==50 \\ Charles R Greathouse IV, Jun 19 2016

A000005(a(n))=50.

A336596 Numbers whose number of divisors is divisible by 7.

Original entry on oeis.org

64, 192, 320, 448, 576, 704, 729, 832, 960, 1088, 1216, 1344, 1458, 1472, 1600, 1728, 1856, 1984, 2112, 2240, 2368, 2496, 2624, 2752, 2880, 2916, 3008, 3136, 3264, 3392, 3520, 3645, 3648, 3776, 3904, 4032, 4160, 4288, 4416, 4544, 4672, 4800, 4928, 5056, 5103

Offset: 1

Amiram Eldar, Jul 26 2020

nonn

The asymptotic density of this sequence is 1 - zeta(7)/zeta(6) = 0.0088404638... (Sathe, 1945).

			64 is a term since A000005(64) = 7 is divisible by 7.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eckford Cohen, Arithmetical Notes, XIII. A Sequal to Note IV, Elemente der Mathematik, Vol. 18 (1963), pp. 8-11.
S. S. Pillai, On a congruence property of the divisor function, J. Indian Math. Soc. (N. S.), Vol. 6, (1942), pp. 118-119.
L. G. Sathe, On a congruence property of the divisor function, American Journal of Mathematics, Vol. 67, No. 3 (1945), pp. 397-406.

Cf. A000005, A008589, A059269, A336595.

Cf. A030516, A113851 and A138031 are subsequences.

q:= n-> is(irem(numtheory[tau](n), 7)=0):
select(q, [$1..5500])[];  # Alois P. Heinz, Jul 26 2020

Select[Range[5000], Divisible[DivisorSigma[0, #], 7] &]

A030516 UNION A030632 UNION A137484 UNION A137491 UNION A175745 UNION A175750 UNION ... - R. J. Mathar, May 05 2023

A274812 Numbers n such that n and n+1 both have 42 divisors.

Original entry on oeis.org

41680575, 146109375, 173996991, 210075200, 301241024, 307619775, 345691071, 387121599, 491184575, 503761599, 580150592, 613216575, 735890624, 960710463, 1079589951, 1182852800, 1187518400, 1406368575, 1413366975

Offset: 1

Charles R Greathouse IV, Jul 08 2016

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Charles R Greathouse IV, GP script to compute terms

Intersection of A005237 and A175750.

PARI
```
is(n)=numdiv(n)==42 && numdiv(n+1)==42
```

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A175756 Numbers with 50 divisors.

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A336596 Numbers whose number of divisors is divisible by 7.

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A274812 Numbers n such that n and n+1 both have 42 divisors.

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