A175495 -id:A175495 - cp's OEIS frontend

A034884 Numbers k such that k < d(k)^2, where d(k) = A000005(k).

2, 3, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 72, 80, 84, 90, 96, 108, 120, 126, 132, 140, 144, 168, 180, 192, 210, 216, 240, 252, 288, 300, 336, 360, 420, 480, 504, 540, 720, 840, 1260

Offset: 1

Erich Friedman

See comment in A175495. - Vladimir Shevelev, May 07 2013
The deficient terms are 2, 3, 4, 8, 10, 14, 15, 16, 32; the first perfect or abundant number not listed is 66 = 2 * 3 * 11; the only term not 7-smooth is 132 = 2^2 * 3 * 11; the largest not divisible by 6 is 140 = 2^2 * 5 * 7. - Peter Munn, Sep 19 2021
The union of this sequence and A276734 has 74 total terms which are all k with floor(sqrt(k)) <= d(k). - Bill McEachen, Apr 07 2023

Cf. A000005, A035033, A035034, A035035, A033950, A036763, A175495, A276734.

Select[Range[1300],#Harvey P. Dale, Apr 11 2014 *)

isok(n) = (n < numdiv(n)^2) \\ Michel Marcus, Jun 07 2013

Labos Elemer added the last three terms and observes that this sequence is now complete.

A056757 Cube of number of divisors is larger than the number.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110

Offset: 1

Labos Elemer, Aug 16 2000

Sequence is finite with 51261 terms. - Charles R Greathouse IV, Apr 27 2011 [Corrected by Amiram Eldar, Jun 02 2024]

The last odd term is a(15199) = 883575. The odd terms are in A056761. - T. D. Noe, May 14 2013

			k = 27935107200 = 128*27*25*7*11*13*17*19 has 3072 divisors, 3072^3/k = 1.03779..., so k is a term.

Charles R Greathouse IV, Table of n, a(n) for n = 1..51261 (complete sequence, corrected by Amiram Eldar)

Cf. A000005, A034884, A035033, A035034, A035035, A056761, A066693.

Cf. A175495 (k < 2^d(k)), A225729-A225738.

t = {}; Do[If[n < DivisorSigma[0,n]^3, AppendTo[t, n]], {n, 10^3}]; t (* T. D. Noe, May 14 2013 *)
Select[Range[120],DivisorSigma[0,#]^3>#&] (* Harvey P. Dale, Apr 22 2019 *)

is(n)=numdiv(n)^3>n \\ Charles R Greathouse IV, Sep 14 2015

{ k : A000005(k)^3 > k}.

A225729 Numbers n such that n < d(n)^(21/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 90, 96, 100, 108, 112, 120, 126, 132, 140, 144, 150, 156, 160, 168, 180, 192, 210, 216, 240, 252, 264, 270, 280, 288, 300, 312, 330, 336, 360, 396

Offset: 1

T. D. Noe, May 14 2013

Alternatively, we could write n^10 < d(n)^21. The last odd number is a(10) = 15.

T. D. Noe, Table of n, a(n) for n = 1..89 (complete sequence)

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).

Cf. A225730-A225738.

t = {}; Do[If[n < DivisorSigma[0, n]^(21/10), AppendTo[t, n]], {n, 10^4}]; t

A225730 Numbers k such that k < d(k)^(22/10), where d(k) is the number of divisors of k.

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 108, 112, 120, 126, 132, 140, 144, 150, 156, 160, 168, 180, 192, 198, 200, 204, 210, 216, 220, 224, 228, 234

Offset: 1

T. D. Noe, May 14 2013

Alternatively, we could write k^5 < d(k)^11. The last odd number is a(23) = 45.

T. D. Noe, Table of n, a(n) for n = 1..155 (complete sequence)

Cf. A000005, A034884 (k < d(k)^2), A175495 (k < 2^d(k)), A056757 (k < d(k)^3).

Cf. A225729-A225738, A353448.

t = {}; Do[If[n < DivisorSigma[0, n]^(22/10), AppendTo[t, n]], {n, 10^5}]; t
Select[Range[250],#Harvey P. Dale, Apr 10 2024 *)

for (k=2, 20000, if (k^5 < numdiv(k)^11, print1(k,", "))) \\ Hugo Pfoertner, Apr 25 2023

A175494 a(n) = floor(n^(1/d(n))), where d(n) = number of divisors of n.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 4, 1, 4, 1, 2, 2, 4, 1, 2, 2, 2, 1, 5, 1, 5, 1, 2, 2, 2, 1, 6, 2, 2, 1, 6, 1, 6, 1, 1, 2, 6, 1, 3, 1, 2, 1, 7, 1, 2, 1, 2, 2, 7, 1, 7, 2, 1, 1, 2, 1, 8, 2, 2, 1, 8, 1, 8, 2, 2, 2, 2, 1, 8, 1, 2, 3, 9, 1, 3, 3, 3

Offset: 1

Leroy Quet, May 30 2010

nonn

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A034884, A175495.

Table[Floor[n^(1/DivisorSigma[0, n])], {n, 100}] (* T. D. Noe, May 14 2013 *)

More terms from R. J. Mathar, May 31 2010

A225737 Numbers n such that n < d(n)^(29/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110

Offset: 1

T. D. Noe, May 14 2013

Alternatively, we could write n^10 < d(n)^29. The last odd term is a(6362) = 225225.

T. D. Noe, Table of n, a(n) for n = 1..21466 (complete sequence)

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).

Cf. A225729-A225738.

t = {}; Do[If[n < DivisorSigma[0, n]^(29/10), AppendTo[t, n]], {n, 10^7}]; t

A225731 Numbers n such that n < d(n)^(23/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192

Offset: 1

T. D. Noe, May 14 2013

Alternatively, we could write n^10 < d(n)^23. The last odd number is a(44) = 105.

T. D. Noe, Table of n, a(n) for n = 1..284 (complete sequence)

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).

Cf. A225729-A225738.

t = {}; Do[If[n < DivisorSigma[0, n]^(23/10), AppendTo[t, n]], {n, 10^5}]; t

A225732 Numbers n such that n < d(n)^(24/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 128, 130, 132, 135, 136, 138, 140

Offset: 1

T. D. Noe, May 14 2013

Alternatively, we could write n^5 < d(n)^12. The last odd number is a(95) = 315.

T. D. Noe, Table of n, a(n) for n = 1..528 (complete sequence)

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).

Cf. A225729-A225738.

t = {}; Do[If[n < DivisorSigma[0, n]^(24/10), AppendTo[t, n]], {n, 10^6}]; t

A225733 Numbers n such that n < d(n)^(5/2), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 96, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 128, 130, 132, 135, 136, 138

Offset: 1

T. D. Noe, May 14 2013

Alternatively, we could write n^2 < d(n)^5. The last odd number is a(206) = 945.

T. D. Noe, Table of n, a(n) for n = 1..1018 (complete sequence)

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).

Cf. A225729-A225738.

t = {}; Do[If[n < DivisorSigma[0, n]^(5/2), AppendTo[t, n]], {n, 10^6}]; t

A225734 Numbers n such that n < d(n)^(26/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 128

Offset: 1

T. D. Noe, May 14 2013

Alternatively, we could write n^5 < d(n)^13. The last odd number is a(473) = 3465.

T. D. Noe, Table of n, a(n) for n = 1..2046 (complete sequence)

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).

Cf. A225729-A225738.

t = {}; Do[If[n < DivisorSigma[0, n]^(26/10), AppendTo[t, n]], {n, 10^7}]; t

cp's OEIS Frontend

A034884 Numbers k such that k < d(k)^2, where d(k) = A000005(k).

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A056757 Cube of number of divisors is larger than the number.

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A225729 Numbers n such that n < d(n)^(21/10), where d(n) is the number of divisors of n.

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A225730 Numbers k such that k < d(k)^(22/10), where d(k) is the number of divisors of k.

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A175494 a(n) = floor(n^(1/d(n))), where d(n) = number of divisors of n.

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A225737 Numbers n such that n < d(n)^(29/10), where d(n) is the number of divisors of n.

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A225731 Numbers n such that n < d(n)^(23/10), where d(n) is the number of divisors of n.

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A225732 Numbers n such that n < d(n)^(24/10), where d(n) is the number of divisors of n.

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A225733 Numbers n such that n < d(n)^(5/2), where d(n) is the number of divisors of n.

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