A033845 -id:A033845 - cp's OEIS frontend

A243405 Minimum among the numbers p^(n/p), where p is a prime factor of n.

1, 2, 3, 4, 5, 8, 7, 16, 27, 25, 11, 64, 13, 49, 125, 256, 17, 512, 19, 625, 343, 121, 23, 4096, 3125, 169, 19683, 2401, 29, 15625, 31, 65536, 1331, 289, 16807, 262144, 37, 361, 2197, 390625, 41, 117649, 43, 14641, 1953125, 529, 47, 16777216, 823543, 9765625, 4913, 28561, 53

Offset: 1

Stanislav Sykora, Jun 04 2014

nonn

The setting a(1)=1 is conventional.

Upper bound (for any n): a(n) <= (3^(1/3))^n = A002581^n.

			a(12)=64 because 2^(12/2)=64 is smaller than 3^(12/3)=81.

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Cf. A002581, A092975 (maximum instead of minimum), A033845.

A243405(n)= {my(m,k,p,q);if(n==1,return(1));
  p=factor(n);m=2^n;
  for(k=1,#p[,1],q=p[k,1]^(n\p[k,1]);if(q

For prime p, a(p)=p.
For n>1: When gpf(n)>3 then a(n)=gpf(n)^(n/gpf(n)); otherwise if n is even then a(n)=2^(n/2); otherwise a(n)=3^(n/3).
If n is in A033845, a(n) = 2^(n/2); otherwise a(n) = gpf(n)^(n/gpf(n)). - Franklin T. Adams-Watters, Jun 15 2014

A284037 Primes p such that p-1 and p+1 have two distinct prime factors.

Original entry on oeis.org

11, 13, 19, 23, 37, 47, 53, 73, 97, 107, 163, 193, 383, 487, 577, 863, 1153, 2593, 2917, 4373, 8747, 995327, 1492993, 1990657, 5308417, 28311553, 86093443, 6879707137, 1761205026817, 2348273369087, 5566277615617, 7421703487487, 21422803359743, 79164837199873

Offset: 1

Giuseppe Coppoletta, Mar 28 2017

nonn

Either p-1 or p+1 must be of the form 2^i * 3^j, since among three consecutive numbers exactly one is a multiple of 3. - Giovanni Resta, Mar 29 2017

Subsequence of A219528. See the previous comment. - Jason Yuen, Mar 08 2025

			7 is not a term because n + 1 = 8 has only one prime factor.
23 is a term because it is prime and n - 1 = 22 has two distinct prime factors (2, 11) and n + 1 = 24 has two distinct prime factors (2, 3).
43 is not a term because n - 1 = 42 has three distinct prime factors (2, 3, 7).

Robert Israel, Table of n, a(n) for n = 1..51 (all terms < 10^75)

Cf. A000668, A001221, A005105, A005109, A033845, A058383, A067386, A092506, A215504, A219528, A275598.

N:= 10^20: # To get all terms <= N
Res:= {}:
for i from 1 to ilog2(N) do
  for j from 1 to floor(log[3](N/2^i)) do
    q:= 2^i*3^j;
    if isprime(q-1) and nops(numtheory:-factorset((q-2)/2^padic:-ordp(q-2,2)))=1 then Res:= Res union {q-1} fi;
    if isprime(q+1) and nops(numtheory:-factorset((q+2)/2^padic:-ordp(q+2,2)))=1 then Res:= Res union {q+1} fi
od od:
sort(convert(Res,list)); # Robert Israel, Apr 16 2017

mx = 10^30; ok[t_] := PrimeQ[t] && PrimeNu[t-1]==2==PrimeNu[t+1]; Sort@ Reap[Do[ w = 2^i 3^j; Sow /@ Select[ w+ {1,-1}, ok], {i, Log2@ mx}, {j, 1, Log[3, mx/2^i]}]][[2, 1]] (* terms up to mx, Giovanni Resta, Mar 29 2017 *)

isok(n) = isprime(n) && (omega(n-1)==2) && (omega(n+1)==2); \\ Michel Marcus, Apr 17 2017

omega=sloane.A001221; [n for n in prime_range(10^6) if 2==omega(n-1)==omega(n+1)]

sorted([2^i*3^j+k for i in (1..40) for j in (1..20) for k in (-1,1) if is_prime(2^i*3^j+k) and sloane.A001221(2^i*3^j+2*k)==2])

A001221(a(n)) = 1 and A001221(a(n) - 1) = A001221(a(n) + 1) = 2.

a(33)-a(34) from Giovanni Resta, Mar 29 2017

A333352 a(n) is the product of indices of the smallest and greatest prime factors of n.

Original entry on oeis.org

1, 1, 4, 1, 9, 2, 16, 1, 4, 3, 25, 2, 36, 4, 6, 1, 49, 2, 64, 3, 8, 5, 81, 2, 9, 6, 4, 4, 100, 3, 121, 1, 10, 7, 12, 2, 144, 8, 12, 3, 169, 4, 196, 5, 6, 9, 225, 2, 16, 3, 14, 6, 256, 2, 15, 4, 16, 10, 289, 3, 324, 11, 8, 1, 18, 5, 361, 7, 18, 4, 400, 2, 441, 12, 6, 8, 20, 6, 484, 3

Offset: 1

Ilya Gutkovskiy, Mar 15 2020

nonn

			a(315) = a(3^2 * 5 * 7) = a(prime(2)^2 * prime(3) * prime(4)) = 2 * 4 = 8.

Cf. A000079 (positions of 1's), A000720, A002110, A006530, A020639, A033845 (positions of 2's), A055396, A061395, A066048, A156061, A243055.

a[1] = 1; a[n_] := PrimePi[FactorInteger[n] [[1, 1]]] PrimePi[ FactorInteger[ n] [[-1, 1]]]; Table[a[n], {n, 1, 80}]

a(n) = if (n==1, 1, my(f=factor(n)[,1]); primepi(vecmin(f))*primepi(vecmax(f))); \\ Michel Marcus, Mar 16 2020

If n = Product (p_j^k_j) then a(n) = min{pi(p_j)} * max{pi(p_j)}, where pi = A000720.
a(n) = A055396(n) * A061395(n) for n > 1.
a(2*n) = A061395(n) for n > 1.
a(n^k) = a(n) for k > 0
a(2*prime(n)^k) = n for k > 0.
a(prime(n)^k) = n^2 for k > 0.
a(n!) = pi(n) for n > 1.
a(A002110(n)) = n.

A339794 a(n) is the least integer k satisfying rad(k)^2 < sigma(k) and whose prime factors set is the same as the prime factors set of A005117(n+1).

Original entry on oeis.org

4, 9, 25, 18, 49, 80, 121, 169, 112, 135, 289, 361, 441, 352, 529, 416, 841, 360, 961, 891, 1088, 875, 1369, 1216, 1053, 1681, 672, 1849, 1472, 2209, 2601, 2809, 3025, 3249, 1856, 3481, 3721, 1984, 4225, 1584, 4489, 4761, 1960, 5041, 5329, 4736, 5929, 2496, 6241

Offset: 1

Michel Marcus, Dec 17 2020

nonn

Equivalently, subsequence of terms of A339744 excluding terms whose prime factor set has already been encountered.
a(n) = A005117(n + 1)^2 when A005117(n + 1) is prime. Proof: if A005117(n + 1) is a prime p then rad(A005117(n + 1))^2 = rad(p)^2 = p^2 and so integers whose prime factors set is the same as the prime factors set of A005117(n + 1) = p are p^m where m >= 1. p^2 > sigma(p^1) = p + 1 but p^2 < sigma(p^2) = p^2 + p + 1. Q.E.D. - David A. Corneth, Dec 19 2020
From Bernard Schott, Jan 19 2021: (Start)
Indeed, a(n) satisfies the double inequality A005117(n+1) < a(n) <= A005117(n+1)^2.
It is also possible that a(n) = A005117(n+1)^2, even when A005117(n+1) is not prime; the smallest such example is for a(13) = 441 = 21^2 = A005117(14)^2. (End)

			   n  a(n) prime factor set
   1    4  [2]           A000079
   2    9  [3]           A000244
   3   25  [5]           A000351
   4   18  [2, 3]        A033845
   5   49  [7]           A000420
   6   80  [2, 5]        A033846
   7  121  [11]          A001020
   8  169  [13]          A001022
   9  112  [2, 7]        A033847
  10  135  [3, 5]        A033849
  11  289  [17]          A001026
  12  361  [19]          A001029
  13  441  [3, 7]        A033850
  14  352  [2, 11]       A033848
  15  529  [23]          A009967
  16  416  [2, 13]       A288162
  17  841  [29]          A009973
  18  360  [2, 3, 5]     A143207

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Michel Marcus)

Cf. A000203 (sigma), A007947 (rad).
Cf. A005117 (squarefree numbers), A027748, A265668, A339744.
Subsequence: A001248 (squares of primes).

u(n) = {my(fn=factor(n)[,1]); for (k = n, n^2, my(fk = factor(k)); if (fk[,1] == fn, if (factorback(fk[,1])^2 < sigma(fk), return (k));););}
lista(nn) = {for (n=2, nn, if (issquarefree(n), print1(u(n), ", ");););}

a(n) <= A005117(n+1)^2. - David A. Corneth, Dec 19 2020

A362948 Numbers whose sum of (distinct) prime divisors (A008472) equals 5.

Original entry on oeis.org

5, 6, 12, 18, 24, 25, 36, 48, 54, 72, 96, 108, 125, 144, 162, 192, 216, 288, 324, 384, 432, 486, 576, 625, 648, 768, 864, 972, 1152, 1296, 1458, 1536, 1728, 1944, 2304, 2592, 2916, 3072, 3125, 3456, 3888, 4374, 4608, 5184, 5832, 6144, 6912, 7776, 8748, 9216, 10368, 11664, 12288

Offset: 1

M. F. Hasler, Jul 20 2023

Amiram Eldar, Table of n, a(n) for n = 1..1000

Cf. A008472 (sopf), A000351 (5^n), A033845 (2^m*3^n).

seq[max_] := Union[Join[5^Range[Floor[Log[5, max]]], Flatten@ Table[2^i*3^j, {i, 1, Log2[max]}, {j, 1, Log[3, max/2^i]}]]]; seq[13000] (* Amiram Eldar, Jul 27 2023 *)

select( {is_A362948(n)=vecsum(factor(n,0)[,1])==5}, [1..11^4]) \\ alternatively: [n | n<-[1..11^4], A008472(n)==5]

Union of A000351 = {5^k ; k > 0} and A033845 = {2^j*3^k, j,k > 0}.

Sum_{n>=1} 1/a(n) = 3/4. - Amiram Eldar, Jul 27 2023

A370266 Numbers k that are not prime powers, such that k/rad(k) >= rad(k), where rad(k) = A007947(k).

Original entry on oeis.org

36, 48, 54, 72, 96, 100, 108, 144, 160, 162, 192, 196, 200, 216, 224, 225, 250, 288, 320, 324, 375, 384, 392, 400, 405, 432, 441, 448, 484, 486, 500, 567, 576, 640, 648, 675, 676, 686, 704, 768, 784, 800, 832, 864, 896, 900, 960, 968, 972, 1000, 1029, 1080, 1089

Offset: 1

Michael De Vlieger, Feb 18 2024

Numbers k = m * s, where s is composite and squarefree, rad(m) | s, and m >= s.

A177492 is a proper subset.

			For s = 6, this sequence contains {36, 48, 54, 72, 96, ...}, i.e., A033845(n) for n >= A010846(6).
For s = 10, this sequence contains {100, 160, 200, 250, 320, ...}, i.e., A033846(n) for n >= A010846(10).
For s = 14, this sequence contains {196, 224, 392, 448, 686, ...}, i.e., A033847(n) for n >= A010846(14).
For s = 15, this sequence contains {225, 375, 405, 675, 1125, ...}, i.e., A033849(n) for n >= A010846(15), etc.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A007947, A010846, A024619, A120944, A126706, A177492, A246547, A286708, A341645, A366250.

Select[Select[Range[2, 1100], Not@*PrimePowerQ], #1/#2 >= #2 & @@ {#, Times @@ FactorInteger[#][[All, 1]]} &]

Set difference of A341645 and A246547.
Intersection of A341645 and A126706.
Union of A286708 and A366250.

A372864 Numbers k such that A372720(k) = 0.

Original entry on oeis.org

1, 500, 578, 722, 750, 1058, 1500, 1682, 1922, 2646, 2744, 3430, 3645, 4800, 5202, 5346, 5476, 5488, 5625, 6318, 6400, 6724, 7168, 7396, 8000, 8836, 10092, 10976, 11236, 11532, 11979, 12005, 13068, 13924, 14450, 14884, 15309, 16810, 16875, 16896, 18050, 18225

Offset: 1

Michael De Vlieger, Jun 02 2024

nonn

Let tau = A000005, let omega = A001221, let f = A008479, and let g = A372720.
For squarefree k, A372720(k) >= 0, since f(k) = 1 while tau(k) = 2^omega(k).
For prime power p^m, A372720(p^m) = 1, since f(p^m) = m while tau(k) = m+1.
Therefore, apart from a(1) = 1, this sequence is a proper subset of A126706.
In the sequence R = {k = m*s : rad(m) | s, s > 1 in A120944}, there is a smallest term k such that g(k) <= 0 and a largest term k such that g(k) is positive. For instance, in A033845 where s = 6, only {6, 12, 18, 24, 36, 48, 54, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864} are such that g(k) > 0.
Apart from terms in this sequence, all the rest of the terms k in R are such that g(k) is negative.
There are no 3-smooth numbers k > 1 in this sequence, however there are 3 terms {500, 6400, 8000} in A033846 (with s = rad(k) = 10). For s = 2*3*23, there are 6 terms {19044, 25392, 38088, 70656, 536544, 953856}.
Conjecture: proper subset of A361098, hence of A360765 and A360768. This is to say that k = a(n) is such that A003557(k) >= A119288(k), i.e., k/rad(k) >= second smallest prime factor of k, and A003557(k) > A053669(k), where A053669(k) is the smallest prime q that does not divide k.

			a(1) = 1 since tau(1) - f(1) = 1 - 1 = 0.
a(2) = 500 = 2^2 * 5*3, since tau(500) - f(500)
     = (2+1)*(3+1) - card({10,20,40,50,80,100,160,200,250,320,400,500})
     = 12 - 12 = 0.
a(3) = 578 = 2*17^2, since tau(578) - f(578)
     = (1+1)*(2+1) - card({34,68,136,272,544,578})
     = 6 - 6 = 0, etc.

Michael De Vlieger, Table of n, a(n) for n = 1..2000

Cf. A000005, A001221, A007947, A008479, A010846, A372720, A372972.

rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; Position[Table[r = rad[n]; DivisorSigma[0, n] - Count[Range[n/r], ?(Divisible[r, rad[#]] &)], {n, 20000}], ?(# == 0 &)][[All, 1]]

A375281 Lexicographically earliest infinite sequence of distinct positive integers such that for all n > 1 a(n-1), a(n) do not have the same number of distinct prime divisors, whereas the squarefree kernel of their product is a primorial number.

Original entry on oeis.org

1, 2, 6, 3, 10, 9, 12, 4, 15, 8, 18, 5, 24, 16, 30, 7, 60, 14, 90, 20, 27, 36, 25, 42, 35, 66, 175, 84, 40, 81, 48, 32, 45, 64, 54, 70, 21, 110, 63, 120, 28, 105, 22, 210, 11, 420, 33, 140, 72, 125, 96, 128, 75, 126, 50, 150, 49, 180, 56, 165, 98, 240, 77, 270

Offset: 1

David James Sycamore, Aug 09 2024

nonn

In other words omega(a(n-1)) != omega(a(n)) whilst rad(a(n-1)*a(n)) is a term in A002110, where omega is A001221 and rad is A007947. In general, primes appear consequent to primorial terms (a(11,12) = 18,5 is an exception). Conjectured to be a permutation of the positive integers, with primes in order.
From Michael De Vlieger, Aug 19 2024: (Start)
Let r be squarefree and define lineage S_r to be the list of numbers k such that rad(k) = r. Then S_r = r*R_r, where R_r is the list of numbers m such that rad(m) | r, hence k = m*r. R_r is the sorted, vectorized tensor product of prime divisor power ranges { p^j : p | r, j >= 0 }. The smallest term of S_r is r itself; it is the only squarefree number in the lineage S_r. S_1 = {1}, but S_r, r > 1 is infinite.
By construction, this sequence features k in S_r in order on account of the squarefree kernel constraint. Example, S_6 = A033845; S_6(1) = a(3) = 6, S_6(2) = a(7) = 12, S_6(3) = a(11) = 18, etc.
Corollary: Prime powers p^j appear in order.
Therefore, if this sequence is a permutation of natural numbers, we should see all squarefree numbers in this sequence, and all k in S_r should appear in order. (End)

			The sequence starts a(1) = 1, a(2) = 2 since this is the earliest pair of positive integers with differing numbers of distinct prime divisors (omega(1) = 0, omega(2) = 1) such that the squarefree kernel rad(1*2) = 2 = A002110(1) is a primorial number.
a(3) = 6 since 3,4,5, all have omega = 1, the same number of distinct prime divisors as 2, but omega(6) = 2 and rad(2*6) = 6 = A002110(2).

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Log log scatterplot of a(n), n = 1..10000, showing primes in red, perfect powers of primes in gold, squarefree composites in green, and numbers neither squarefree nor prime powers in blue and purple, with purple additionally signifying powerful numbers that are not prime powers.
Michael De Vlieger, Fan style binary tree showing n for a(n) = A019565(i), i = 0..511, with a color function where red = 1 and magenta = 10000.
Michael De Vlieger, Log log scatterplot of a(n), n = 1..10^4, with a color function showing omega(a(n)) <= 1 in black, omega(a(n)) = 2 in red, ..., and omega(a(n)) = 9 in blue.

Cf. A001221, A002110, A007947.

Clear[c]; nn = 64; s = {1, 2}; kk = Length[s]; u = 1;
c[_] := False; P = FoldList[Times, 1, Prime@ Range[60] ];
rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
MapIndexed[Set[{a[First[#2]], c[#1]}, {#1, True}] &, s];
Set[{i, j}, {a[kk - 1], a[kk]}]; While[c[u], u++];
Do[k = u;
  While[Or[c[k], FreeQ[P, rad[j*k]], PrimeNu[k] == PrimeNu[j] ], k++];
  Set[{a[n], c[k], i, j}, {k, True, j, k}];
  If[k == u, While[c[u], u++] ], {n, kk + 1, nn}];
Array[a, nn] (* Michael De Vlieger, Aug 19 2024 *)

More terms from Michael De Vlieger, Aug 19 2024

A379713 Array read by downward antidiagonals: rows list practical numbers with the same progenitor primitive practical number (A267124).

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 20, 16, 18, 40, 28, 32, 24, 80, 56, 30, 64, 36, 100, 112, 60, 42, 128, 48, 160, 196, 90, 84, 66, 256, 54, 200, 224, 120, 126, 132, 78, 512, 72, 320, 392, 150, 168, 198, 156, 88, 1024, 96, 400, 448, 180, 252, 264, 234, 176, 104, 2048, 108, 500, 784, 240, 294, 396, 312, 352, 208, 140, 4096, 144, 640, 896, 270, 336, 528, 468, 704, 416, 280, 204, 8192

Offset: 1

Frank M Jackson, Dec 30 2024

A permutation of the practical numbers.
This sequence is presented as an array of rows. The first row contains a single term of value 1. Subsequent rows are infinite sequences and are presented as a square array by listing the antidiagonals downwards that is 1: 2; 4,6; 8,12,20; etc.
The first column contains the primitive practical numbers A267124; each row lists all practical numbers (A005153) having the same primitive practicle progenitor and which is the first term in each row. See A379325 comments for further details. If T[1,m] is squarefree then the row is identical to the same squarefree row in A284457.
Every primitive practical number A267124(n) is the progenitor of a disjoint subsequence of the practical numbers. If the PP column represents the sequence of primitive practical numbers A267124, the table below give the 7 initial terms of the disjoint sequences of practical numbers A005153 generated by the initial 7 terms of the sequence of primitive practical numbers.
PP: Disjoint subsequence of A005153
--  -------------------------------
1:   1
2:   2,  4,  8, 16, 32, 64,128, . . .- A000079 with offset 1,1
6:   6, 12, 18, 24, 36, 48, 54, . . .- A033845
20: 20, 40, 80,100,160,200,320, . . .
28: 28, 56,112,196,224,392,448, . . .
30: 30, 60, 90,120,150,180,240, . . .- A143207
42: 42, 84,126,168,252,294,336
...
Row 1 is T[1,1] = 1 and only has one term in the subsequence.
Row 7 is T[1,7] = 2*3*7; T[2,7] = 2^2*3*7; T[3,7] = 2*3^2*7; T[4,7] = 2^3*3*7; T[5,7] = 2^2*3^2*7, etc.

			a(14) = 80 and it is T[3,4] = 2^4*5. Its primitive progenitor is 20 = 2^2*5 and its equivalence class are the terms of row 4.

Frank M Jackson, Mathematica program

Cf. A000079, A005117, A005153, A007947, A033845, A143207, A267124, A284457, A379325.

Mathematica
```
(* See link above *)
```

A381805 Smallest composite squarefree number that is coprime to n.

Original entry on oeis.org

6, 15, 10, 15, 6, 35, 6, 15, 10, 21, 6, 35, 6, 15, 14, 15, 6, 35, 6, 21, 10, 15, 6, 35, 6, 15, 10, 15, 6, 77, 6, 15, 10, 15, 6, 35, 6, 15, 10, 21, 6, 55, 6, 15, 14, 15, 6, 35, 6, 21, 10, 15, 6, 35, 6, 15, 10, 15, 6, 77, 6, 15, 10, 15, 6, 35, 6, 15, 10, 33, 6, 35

Offset: 1

Michael De Vlieger, Mar 31 2025

Let p be the smallest prime that is coprime to n and let q be the second smallest prime that is coprime to n. Then a(n) = p*q.

Records in this sequence are set by n in A002110.

			a(1) = 6 = 2*3, since p = 2, q = 3.
a(2) = 15 = 3*5, since p = 3, q = 5.
a(3) = 10 = 2*5, since p = 2, q = 5.
a(4) = 15 = 3*5, since p = 3, q = 5, a(2^i) = 15 for i > 0.
a(6) = 35 = 5*7, since p = 5, q = 7.
a(9) = 20 = 2*5, since p = 2, q = 5, a(3^i) = 10 for i > 0.
a(10) = 21 = 3*7, since p = 3, q = 7.
a(12) = 35 = 5*7, since p = 5, q = 7, a(k) = 35 for n in A033845 (i.e., n such that rad(n) = 6).
a(20) = 21 = 3*7, since p = 3, q = 7, a(k) = 21 for n in A033846 (i.e., n such that rad(n) = 10).
a(30) = 77 = 7*11, since p = 7, q = 11, etc.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A002110, A007947, A051250, A053669, A120944, A380539, A382248.

Table[c = 0; q = 2; Times @@ Reap[While[c < 2, While[Divisible[n, q], q = NextPrime[q]]; Sow[q]; q = NextPrime[q]; c++] ][[-1, 1]], {n, 120}]

a(n) = my(k=2); while (isprime(k) || !issquarefree(k) || (gcd(k, n) != 1) , k++); k; \\ Michel Marcus, Apr 01 2025

a(n) = A053669(n) * A380539(n) = A382248(n)/A020639(n).
For k and m such that rad(k) = rad(m), a(k) = a(m), where rad = A007947.
n < a(n) for n in A051250, a finite sequence whose largest term is 60.

cp's OEIS Frontend

A243405 Minimum among the numbers p^(n/p), where p is a prime factor of n.

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A284037 Primes p such that p-1 and p+1 have two distinct prime factors.

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A333352 a(n) is the product of indices of the smallest and greatest prime factors of n.

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A339794 a(n) is the least integer k satisfying rad(k)^2 < sigma(k) and whose prime factors set is the same as the prime factors set of A005117(n+1).

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A362948 Numbers whose sum of (distinct) prime divisors (A008472) equals 5.

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A370266 Numbers k that are not prime powers, such that k/rad(k) >= rad(k), where rad(k) = A007947(k).

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A372864 Numbers k such that A372720(k) = 0.

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