A030638 -id:A030638 - cp's OEIS frontend

A036457 Numbers k for which exactly 5 applications of A000005 are needed to reach 2.

60, 72, 84, 90, 96, 108, 126, 132, 140, 150, 156, 160, 180, 198, 200, 204, 220, 224, 228, 234, 240, 252, 260, 276, 288, 294, 300, 306, 308, 315, 336, 340, 342, 348, 350, 352, 360, 364, 372, 380, 392, 396, 414, 416, 420, 432, 444, 450, 460, 468, 476, 480

Offset: 1

Labos Elemer

nonn

Subsequences include A030630 (numbers with 12 divisors), A030636 (numbers with 18 divisors), A030638 (numbers with 20 divisors), A137491 (numbers with 28 divisors), etc. [edited by Jon E. Schoenfield, May 12 2018]

			a(13)=180; the successive iterates are 18, 6, 4, 3, and finally the 5th is 2;
a(3)=84; divisor numbers are 12, 6, 4, 3, and 2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000005, A007624, A036450, A036452, A036453, A036455, A030630.

A036459:= proc(n) option remember;
  if n <= 2 then 0 else 1 + procname(numtheory:-tau(n)) fi
end proc:
select(A036459 = 5, [$1..1000]); # Robert Israel, Jan 25 2016

Select[Range@ 480, Last@ # == 2 && #[[5]] != 2 &@ NestList[DivisorSigma[0, #] &, #, 5] &] (* Michael De Vlieger, Jan 26 2016 *)

is(n)=for(i=1,4,n=numdiv(n); if(n<3, return(0))); numdiv(n)==2 \\ Charles R Greathouse IV, Sep 17 2015

d(d(d(d(d(a(n)))))) = 2 for all n.

A036459(a(n)) = 5. - Ivan Neretin, Jan 25 2016

New name from Robert Israel, Jan 25 2016

A137487 Numbers with 24 divisors.

Original entry on oeis.org

360, 420, 480, 504, 540, 600, 630, 660, 672, 756, 780, 792, 864, 924, 936, 990, 1020, 1050, 1056, 1092, 1120, 1140, 1152, 1170, 1176, 1188, 1224, 1248, 1350, 1368, 1380, 1386, 1400, 1404, 1428, 1470, 1500, 1530, 1540, 1596, 1632, 1638, 1650, 1656, 1710

Offset: 1

R. J. Mathar, Apr 22 2008

nonn

Maple implementation: see A030513.

Numbers of the form p^23, p^2*q^7, p*q^2*r^3 (like 360, 504), p*q*r^5 (like 480, 672), p*q*r*s^2 (like 420, 660), p^3*q^5 (like 864) or p*q^11, where p, q, r and s are distinct primes. - R. J. Mathar, Mar 01 2010

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A030513-A030516, A030626, A030627, A030634-A030638, A005179, A003680, A096932, A061286, A061283.

Select[Range[3000],DivisorSigma[0,#]==24&] (* Vladimir Joseph Stephan Orlovsky, May 05 2011 *)

is(n)=numdiv(n)==24 \\ Charles R Greathouse IV, Jun 19 2016

A000005(a(n))=24.

A137489 Numbers with 26 divisors.

Original entry on oeis.org

12288, 20480, 28672, 45056, 53248, 69632, 77824, 94208, 118784, 126976, 151552, 167936, 176128, 192512, 217088, 241664, 249856, 274432, 290816, 299008, 323584, 339968, 364544, 397312, 413696, 421888, 438272, 446464, 462848, 520192, 536576

Offset: 1

R. J. Mathar, Apr 22 2008

nonn

Maple implementation: see A030513.

Numbers of the form p^25 (5th powers of A050997, subset of A010813) or p*q^12, where p and q are distinct primes. - R. J. Mathar, Mar 01 2010

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A030513-A030516, A030626, A030627, A030634-A030638, A005179, A003680, A096932, A061286, A061283.

Select[Range[900000],DivisorSigma[0,#]==26&] (* Vladimir Joseph Stephan Orlovsky, May 05 2011 *)

is(n)=numdiv(n)==26 \\ Charles R Greathouse IV, Jun 19 2016

A000005(a(n))=26.

A274361 Numbers n such that n and n+1 both have 20 divisors.

Original entry on oeis.org

5264, 7695, 13040, 27135, 33615, 38960, 41391, 44144, 54351, 55808, 62127, 64719, 70064, 72495, 77679, 100624, 101007, 108783, 108944, 116720, 124335, 124496, 132111, 132272, 139887, 145232, 160784, 165807, 176336, 186704, 191888, 199375, 202095

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 A030638.

Cf. A000005, A274357.

PARI
```
is(n)=numdiv(n)==20 && numdiv(n+1)==20
```

A137490 Numbers with 27 divisors.

Original entry on oeis.org

900, 1764, 2304, 4356, 4900, 6084, 6400, 10404, 11025, 12100, 12544, 12996, 16900, 19044, 23716, 26244, 27225, 28900, 30276, 30976, 33124, 34596, 36100, 38025, 43264, 49284, 52900, 53361, 56644, 60516, 65025, 66564, 70756, 73984, 74529

Offset: 1

R. J. Mathar, Apr 22 2008

nonn

Maple implementation: see A030513.

Numbers of the form p^26 (subset of A089081), p^2*q^2*r^2 (like 900, 1764, 4356, squares of A007304) or p^2*q^8 (like 2304, 6400, subset of the squares of A030628) where p, q and r are distinct primes. - R. J. Mathar, Mar 01 2010

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000005, A030513-A030516, A030626, A030627, A030634-A030638, A005179, A003680, A096932, A061286, A061283.

Select[Range[150000],DivisorSigma[0,#]==27&] (* Vladimir Joseph Stephan Orlovsky, May 06 2011 *)

isA137490(n) = numdiv(n)==27 \\ Michael B. Porter, Apr 10 2010

A000005(a(n)) = 27.

Sum_{n>=1} 1/a(n) = (P(2)^3 + 2*P(6) - 3*P(2)*P(4))/6 + P(2)*P(8) - P(10) + P(26) = 0.00453941..., where P is the prime zeta function. - Amiram Eldar, Jul 03 2022

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A036457 Numbers k for which exactly 5 applications of A000005 are needed to reach 2.

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A137487 Numbers with 24 divisors.

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A137489 Numbers with 26 divisors.

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A274361 Numbers n such that n and n+1 both have 20 divisors.

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A137490 Numbers with 27 divisors.

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