A033851 -id:A033851 - cp's OEIS frontend

A033848 Numbers whose prime factors are 2 and 11.

22, 44, 88, 176, 242, 352, 484, 704, 968, 1408, 1936, 2662, 2816, 3872, 5324, 5632, 7744, 10648, 11264, 15488, 21296, 22528, 29282, 30976, 42592, 45056, 58564, 61952, 85184, 90112, 117128, 123904, 170368, 180224, 234256, 247808, 322102

Offset: 1

Jeff Burch

nonn

Numbers k such that phi(k)/k = 5/11. - Michel Marcus, Sep 22 2012

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A033845, A033846, A033847, A033849, A033850, A033851, A143201.

import Data.Set (singleton, deleteFindMin, insert)
a033848 n = a033848_list !! (n-1)
a033848_list = f (singleton (2*11)) where
   f s = m : f (insert (2*m) $ insert (11*m) s') where
     (m,s') = deleteFindMin s
-- Reinhard Zumkeller, Sep 13 2011

N:= 10^6: # to get all terms <= N
S:= {seq(seq(2^i*11^j, i=1..ilog2(floor(N/11^j))),j=1..floor(log[11](N/2)))}:
sort(convert(S,list)); # Robert Israel, Oct 26 2017

Select[Range[10^6], FactorInteger[#][[All, 1]] == {2, 11} &] (* Michael De Vlieger, Oct 26 2017 *)
Sort[Flatten[Table[Table[2^j 11^k, {j, 1, 8}], {k, 1, 8}]]] (* Vincenzo Librandi, Oct 27 2017 *)

A143201(a(n)) = 10. - Reinhard Zumkeller, Sep 13 2011

Sum_{n>=1} 1/a(n) = 1/10. - Amiram Eldar, Dec 22 2020

A288162 Numbers whose prime factors are 2 and 13.

Original entry on oeis.org

26, 52, 104, 208, 338, 416, 676, 832, 1352, 1664, 2704, 3328, 4394, 5408, 6656, 8788, 10816, 13312, 17576, 21632, 26624, 35152, 43264, 53248, 57122, 70304, 86528, 106496, 114244, 140608, 173056, 212992, 228488, 281216, 346112, 425984, 456976, 562432, 692224, 742586, 851968, 913952

Offset: 1

Bernard Schott, Jun 06 2017

nonn

Numbers k such that phi(k)/k = 6/13.

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

Cf. A033845, A033846, A033847, A033848, A033849, A033850, A033851, A086780, A107326, A143207.

[n:n in [1..100000] | Set(PrimeDivisors(n)) eq {2,13}];  // Marius A. Burtea, May 10 2019

Select[Range[920000],FactorInteger[#][[All,1]]=={2,13}&] (* Harvey P. Dale, Jun 18 2021 *)

is(n) = factor(n)[, 1]~==[2, 13] \\ Felix Fröhlich, Jun 06 2017

list(lim)=my(v=List(),t); for(n=1,logint(lim\2,13), t=13^n; while((t<<=1)<=lim, listput(v,t))); Set(v) \\ Charles R Greathouse IV, Jun 11 2017

a(n) = 26 * A107326(n). - David A. Corneth, Jun 06 2017

Sum_{n>=1} 1/a(n) = 1/12. - Amiram Eldar, Dec 22 2020

A343300 a(n) is p1^1 + p2^2 + ... + pk^k where {p1,p2,...,pk} are the distinct prime factors in ascending order in the prime factorization of n.

Original entry on oeis.org

0, 2, 3, 2, 5, 11, 7, 2, 3, 27, 11, 11, 13, 51, 28, 2, 17, 11, 19, 27, 52, 123, 23, 11, 5, 171, 3, 51, 29, 136, 31, 2, 124, 291, 54, 11, 37, 363, 172, 27, 41, 354, 43, 123, 28, 531, 47, 11, 7, 27, 292, 171, 53, 11, 126, 51, 364, 843, 59, 136, 61, 963, 52, 2, 174, 1342, 67, 291, 532, 370, 71, 11, 73

Offset: 1

Giorgos Kalogeropoulos, Apr 11 2021

nonn

From Bernard Schott, May 07 2021: (Start)
a(n) depends only on prime factors of n (see formulas).
Primes are fixed points of this sequence.
Terms are in increasing order in A344023. (End)

			a(60) = 136 because the distinct prime factors of 60 are {2, 3, 5} and 2^1 + 3^2 + 5^3 = 136.

Michel Marcus, Table of n, a(n) for n = 1..10000

Cf. A027748, A344023 (terms ordered).

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A033848 Numbers whose prime factors are 2 and 11.

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A288162 Numbers whose prime factors are 2 and 13.

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A343300 a(n) is p1^1 + p2^2 + ... + pk^k where {p1,p2,...,pk} are the distinct prime factors in ascending order in the prime factorization of n.

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Programs

Maple

Mathematica

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