A036967 -id:A036967 - cp's OEIS frontend

A069493 6-full numbers: if p divides n then so does p^6.

1, 64, 128, 256, 512, 729, 1024, 2048, 2187, 4096, 6561, 8192, 15625, 16384, 19683, 32768, 46656, 59049, 65536, 78125, 93312, 117649, 131072, 139968, 177147, 186624, 262144, 279936, 373248, 390625, 419904, 524288, 531441, 559872, 746496, 823543, 839808

Offset: 1

Benoit Cloitre, Apr 15 2002

a(m) mod prime(n) > 0 for m < A258603(n); a(A258600(n)) = A030516(n) = prime(n)^6. - Reinhard Zumkeller, Jun 06 2015

			2^7*3^6 = 93312 is a member (although not of A076470).

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A036967, A036966, A001694. Different from A076470.

Cf. A030516, A258603.

import Data.Set (singleton, deleteFindMin, fromList, union)
a069493 n = a069493_list !! (n-1)
a069493_list = 1 : f (singleton z) [1, z] zs where
   f s q6s p6s'@(p6:p6s)
     | m < p6 = m : f (union (fromList $ map (* m) ps) s') q6s p6s'
     | otherwise = f (union (fromList $ map (* p6) q6s) s) (p6:q6s) p6s
     where ps = a027748_row m
           (m, s') = deleteFindMin s
   (z:zs) = a030516_list
-- Reinhard Zumkeller, Jun 03 2015

Join[{1},Select[Range[900000],Min[FactorInteger[#][[All,2]]]>5&]] (* Harvey P. Dale, Mar 03 2018 *)

for(n=1,560000,if(n*sumdiv(n,d,isprime(d)/d^6)==floor(n*sumdiv(n,d,isprime(d)/d^6)),print1(n,",")))

from math import gcd
from sympy import factorint, integer_nthroot
def A069493(n):
    def f(x):
        c = n+x
        for y1 in range(1,integer_nthroot(x,11)[0]+1):
            if all(d<=1 for d in factorint(y1).values()):
                for y2 in range(1,integer_nthroot(z2:=x//y1**11,10)[0]+1):
                    if gcd(y2,y1)==1 and all(d<=1 for d in factorint(y2).values()):
                        for y3 in range(1,integer_nthroot(z3:=z2//y2**10,9)[0]+1):
                            if gcd(y3,y1)==1 and gcd(y3,y2)==1 and all(d<=1 for d in factorint(y3).values()):
                                for y4 in range(1,integer_nthroot(z4:=z3//y3**9,8)[0]+1):
                                    if gcd(y4,y1)==1 and gcd(y4,y2)==1 and gcd(y4,y3)==1 and all(d<=1 for d in factorint(y4).values()):
                                        for y5 in range(1,integer_nthroot(z5:=z4//y4**8,7)[0]+1):
                                            if gcd(y5,y1)==1 and gcd(y5,y2)==1 and gcd(y5,y3)==1 and gcd(y5,y4)==1 and all(d<=1 for d in factorint(y5).values()):
                                                c -= integer_nthroot(z5//y5**7,6)[0]
        return c
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    return bisection(f,n,n) # Chai Wah Wu, Sep 10 2024

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p^5*(p-1))) = 1.0334657852594050612296726462481884631303137561267151463866539131591664... - Amiram Eldar, Jul 09 2020

A258569 Smallest prime factors of 4-full numbers, a(1)=1.

Original entry on oeis.org

1, 2, 2, 2, 3, 2, 3, 2, 2, 5, 3, 2, 2, 2, 3, 7, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 2, 11, 2, 5, 2, 7, 3, 2, 2, 2, 13, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 5, 2, 2, 17, 2, 2, 2, 7, 2, 19, 2, 2, 3, 2, 2, 11, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 23, 2, 2, 2, 2

Offset: 1

Reinhard Zumkeller, Jun 06 2015

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (some terms corrected by Georg Fischer)

Cf. A036967, A020639, A258601, A258567, A258568, A258570, A258571.

Haskell
```
a258569 = a020639 . a036967
```

Reap[Sow[1]; Do[f = FactorInteger[k]; If[Min[f[[All, 2]]] >= 4, Sow[f[[1, 1]]]], {k, 2, 10^6}]][[2, 1]] (* Jean-François Alcover, Sep 29 2020 *)

lista(kmax) = {my(f); print1(1, ", "); for(k = 2, kmax, f = factor(k); if(vecmin(f[, 2]) > 3, print1(f[1, 1], ", ")));} \\ Amiram Eldar, Sep 09 2024

a(n) = A020639(A036967(n));

a(A258601(n)) = A000040(n) and a(m) != A000040(n) for m < A258601(n).

A385049 The sum of the unitary divisors of n that are biquadratefree numbers (A046100).

Original entry on oeis.org

1, 3, 4, 5, 6, 12, 8, 9, 10, 18, 12, 20, 14, 24, 24, 1, 18, 30, 20, 30, 32, 36, 24, 36, 26, 42, 28, 40, 30, 72, 32, 1, 48, 54, 48, 50, 38, 60, 56, 54, 42, 96, 44, 60, 60, 72, 48, 4, 50, 78, 72, 70, 54, 84, 72, 72, 80, 90, 60, 120, 62, 96, 80, 1, 84, 144, 68, 90

Offset: 1

Amiram Eldar, Jun 16 2025

First differs from A383763 at n = 32.

The number of these divisors is A365499(n), and the largest of them is A385007(n).

D. Suryanarayana, The number and sum of k-free integers <= x which are prime to n, Indian J. Math., Vol. 11 (1969), pp. 131-139.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Francesco Pappalardi, A survey on k-freeness, Number Theory, Ramanujan Math. Soc. Lect. Notes Ser., Vol. 1 (2003), pp. 71-88.

The unitary analog of A385006.
Cf. A036967, A046100, A365499, A385007.
The sum of unitary divisors of n that are: A092261 (squarefree), A192066 (odd), A358346 (exponentially odd), A358347 (square), A360720 (powerful), A371242 (cubefree), A380396 (cube), A383763 (exponentially squarefree), A385043 (exponentially 2^n), A385045 (5-rough), A385046 (3-smooth), A385047 (power of 2), A385048 (cubefull), this sequence (biquadratefree).

f[p_, e_] := If[e < 4, p^e + 1, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] < 4, f[i, 1]^f[i, 2] + 1, 1)); }

Multiplicative with a(p^e) = p^e + 1 for e <= 3, and a(p^e) = 1 for e >= 4.
a(n) = 1 if and only if n is 4-full (A036967).
a(n) <= A034448(n), with equality if and only if n is biquadratefree.
Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + 1/p^(s-1) + 1/p^(2*s-2) - 1/p^(2*s-1) + 1/p^(3*s-3) - 1/p^(3*s-2) - 1/p^(4*s-3)).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 + 1/(p^2 + p) - 1/p^4) = 1.27769267395905900191... .

A076468 Perfect powers m^k where k >= 4.

Original entry on oeis.org

1, 16, 32, 64, 81, 128, 243, 256, 512, 625, 729, 1024, 1296, 2048, 2187, 2401, 3125, 4096, 6561, 7776, 8192, 10000, 14641, 15625, 16384, 16807, 19683, 20736, 28561, 32768, 38416, 46656, 50625, 59049, 65536, 78125, 83521, 100000, 104976, 117649

Offset: 1

Robert G. Wilson v, Oct 14 2002

nonn

If p|n then at least p^4|n.

Subsequence of A036967. - R. J. Mathar, May 27 2011

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

Cf. A001597, A036967, A076467, A076469, A076470.

Cf. A002117, A013661.

import qualified Data.Set as Set (null)
import Data.Set (empty, insert, deleteFindMin)
a076468 n = a076468_list !! (n-1)
a076468_list = 1 : f [2..] empty where
   f xs'@(x:xs) s | Set.null s || m > x ^ 4 = f xs $ insert (x ^ 4, x) s
                  | m == x ^ 4  = f xs s
                  | otherwise = m : f xs' (insert (m * b, b) s')
                  where ((m, b), s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 19 2013

a = {1}; Do[ If[ Apply[ GCD, Last[ Transpose[ FactorInteger[n]]]] > 3, a = Append[a, n]; Print[n]], {n, 2, 131071}]; a

from sympy import mobius, integer_nthroot
def A076468(n):
    def f(x): return int(n+2+x-integer_nthroot(x,4)[0]-(integer_nthroot(x,6)[0]<<1)-integer_nthroot(x,9)[0]+sum(mobius(k)*(integer_nthroot(x,k)[0]+integer_nthroot(x,k<<1)[0]+integer_nthroot(x,3*k)[0]-3) for k in range(5,x.bit_length())))
    kmin, kmax = 1,2
    while f(kmax) >= kmax:
        kmax <<= 1
    while True:
        kmid = kmax+kmin>>1
        if f(kmid) < kmid:
            kmax = kmid
        else:
            kmin = kmid
        if kmax-kmin <= 1:
            break
    return kmax # Chai Wah Wu, Aug 14 2024

Sum_{n>=1} 1/a(n) = 3 - zeta(2) - zeta(3) + Sum_{k>=2} mu(k)*(3 - zeta(k) - zeta(2*k) - zeta(3*k)) = 1.1473274274... . - Amiram Eldar, Dec 03 2022

A377022 Numbers whose prime factorization has exponents that have no digit 1 in their factorial-base representation (A255411).

Original entry on oeis.org

1, 16, 81, 625, 1296, 2401, 4096, 10000, 14641, 28561, 38416, 50625, 65536, 83521, 130321, 194481, 234256, 262144, 279841, 331776, 456976, 531441, 707281, 810000, 923521, 1185921, 1336336, 1500625, 1874161, 2085136, 2313441, 2560000, 2825761, 3111696, 3418801

Offset: 1

Amiram Eldar, Oct 13 2024

Numbers that are "powerful" when they are factorized into factors of the form p^(k!), where p is a prime and k >= 1, a factorization that is done using the factorial-base representation of the exponents in the prime factorization (see A376885 for more details). Each factor p^(k!) has a multiplicity that is larger than 1.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A255411, A376885, A377019, A377020, A377021.
Analogous to A001694.
Subsequence of A036967.

expQ[n_] := expQ[n] = Module[{k = n, m = 2, r, s = 1}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, If[r == 1, s = 0; Break[]]; m++]; s == 1]; seq[lim_] := Module[{p = 2, s = {1}, emax, es}, While[(emax = Floor[Log[p, lim]]) > 3, es = Select[Range[0, emax], expQ]; s = Union[s, Select[Union[Flatten[Outer[Times, s, p^es]]], # <= lim &]]; p = NextPrime[p]]; s]; seq[4*10^6]

isexp(n) = {my(k = n, m = 2, r); while([k, r] = divrem(k, m); k != 0 || r != 0, if(r == 1, return(0)); m++); 1;}
is(k) = {my(e = factor(k)[, 2]); for(i = 1, #e, if(!isexp(e[i]), return(0))); 1;}

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=1} 1/p^A255411(k)) = 1.07819745085315583226... .

A297075 Lexicographically earliest sequence of distinct positive numbers such that the prime factorizations of two consecutive terms never share a prime exponent >= 1.

Original entry on oeis.org

1, 2, 4, 3, 8, 5, 9, 6, 16, 7, 25, 10, 27, 11, 32, 12, 64, 13, 36, 14, 49, 15, 72, 17, 81, 18, 125, 19, 100, 21, 108, 22, 121, 23, 128, 20, 216, 26, 144, 24, 169, 29, 196, 30, 200, 31, 225, 33, 243, 28, 256, 34, 288, 35, 289, 37, 324, 38, 343, 39, 361, 40, 400

Offset: 1

Rémy Sigrist, Dec 25 2017

nonn

For any n > 0, if a prime number p divides a(n) and a prime number q divides a(n+1), then the p-adic valuation of a(n) differs from the q-adic valuation of a(n+1).
Equivalently, for any n > 0, A297404(a(n)) AND A297404(a(n+1)) = 0 (where AND denotes the bitwise AND operator).
This sequence is a permutation of the natural numbers, with inverse A297403.
The curves visible in the logarithmic scatterplot of the first terms seems to be related to a(n) belonging to A038109 and to A052485 (see Links section).
Lexicographically earliest sequence of distinct numbers such that gcd(A181819(a(n)), A181819(a(n+1))) = 1. - Peter Munn, Oct 02 2023
From Peter Munn, Jan 25 2024: (Start)
The sequence bisections might be characterized as being monotonic with interruptions. The major interruptions are apparent from the coloring in the author's 15000 term logarithmic scatterplot -- they occur where the occurrence of terms belonging to A038109 switches between the bisections.
Other interruptions are too small to be seen in the scatterplot. Some relate to numbers that have both the square of a prime and cube of a prime as a unitary divisor (a subset of A038109).
Two such terms are a(4154) = 1350 and a(4156) = 1368, interrupting the even bisection's monotonicity after a(4152) = 1380. These 3 terms are each followed by a 4-full number (A036967): a(4153) = 1185921, a(4155) = 1229312, a(4157) = 1250000. Then we see an odd bisection interruption with a(4159) = 1191016.
(End)

			The first terms, alongside the corresponding sets of prime exponents, are:
  n       a(n)    Set of prime exponents of a(n)
  --      ----    ------------------------------
   1       1      {}
   2       2      {1}
   3       4      {2}
   4       3      {1}
   5       8      {3}
   6       5      {1}
   7       9      {2}
   8       6      {1, 1}
   9      16      {4}
  10       7      {1}
  11      25      {2}
  12      10      {1, 1}
  13      27      {3}
  14      11      {1}
  15      32      {5}
  16      12      {2, 1}
  17      64      {6}
  18      13      {1}
  19      36      {2, 2}
  20      14      {1, 1}

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored logarithmic scatterplot of the first 15000 terms
Rémy Sigrist, C++ program for A297075
Index entries for sequences that are permutations of the natural numbers

Cf. A001694 (numbers in odd bisection), A036967, A038109, A052485 (numbers in even bisection), A181819, A297403 (inverse), A297404.

Nest[Append[#, Block[{k = 3, m = FactorInteger[#[[-1]] ][[All, -1]]}, While[Nand[FreeQ[#, k], ! IntersectingQ[m, FactorInteger[k][[All, -1]]]], k++]; k]] &, {1, 2}, 61] (* Michael De Vlieger, Dec 29 2017 *)

A358250 Numbers whose square has a number of divisors coprime to 210.

Original entry on oeis.org

1, 32, 64, 243, 256, 512, 729, 2048, 3125, 6561, 7776, 15552, 15625, 16384, 16807, 19683, 23328, 32768, 46656, 62208, 100000, 117649, 124416, 161051, 177147, 186624, 200000, 209952, 262144, 371293, 373248, 390625, 419904, 497664, 500000, 537824, 629856, 759375

Offset: 1

Michael De Vlieger, Dec 03 2022

nonn

210 is the product of the smallest 4 primes.
Numbers k such that gcd(d(k^2), 210) = 1, where d(k) is the number of divisors of k (A000005).
Also numbers with no exponents = 1 mod 3, 2 mod 5, or 3 mod 7; also numbers whose square has a number of divisors coprime to 105. - Charles R Greathouse IV, Dec 08 2022

Michael De Vlieger, Table of n, a(n) for n = 1..5000

Subsequence of A069492 and hence of A036967, A036966, and A001694.
Subsequence of other sequences of numbers k such that gcd(d(k^2), m) = 1: A350014 (m=6), A354179 (m=30).
Cf. A000005, A000290, A008364.

With[{nn = 2^20}, Select[Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], CoprimeQ[DivisorSigma[0, #^2], 210] &]]

is(n,f=factor(n))=if(n<32, return(n==1)); my(t=f[,2]%105, N=19200959813818273241621521446046); for(i=1,#t, if(bittest(N,t[i]), return(0))); 1 \\ Charles R Greathouse IV, Dec 08 2022

Sum_{n>=1} 1/a(n) = Product_{p prime} (Sum_{k=2..210, gcd(k-1,210)=1} p^(k/2))/(p^105-1) = 1.05981355805... . - Amiram Eldar, Dec 06 2022

A363177 Primitive abundant numbers (A071395) that are cubefull numbers (A036966).

Original entry on oeis.org

26376098024367, 33912126031329, 1910383099764867, 2792098376579421, 5229860083034911875, 6886512413632368153, 8815747507513708671, 28966027524687899919, 42200802302982406288, 89594138836162749375, 224439112362213402759, 288564573037131517833, 512767531125033485625

Offset: 1

Amiram Eldar, May 19 2023

nonn

It seems that this sequence is also the intersection of A036966 and A091191 (checked up to 10^27).

Are there terms that are 4-full numbers (A036967)? There are none below 10^27.

Amiram Eldar, Table of n, a(n) for n = 1..42 (terms below 10^27)
Wikipedia, Primitive abundant number.

Intersection of A036966 and A071395.
Subsequence of A363169 and A363175.
A306797 is a subsequence.
Cf. A036967, A091191.

A372405 Exponentially powerful numbers whose prime factorization exponents are all powerful numbers > 1.

Original entry on oeis.org

1, 16, 81, 256, 512, 625, 1296, 2401, 6561, 10000, 14641, 19683, 20736, 28561, 38416, 41472, 50625, 65536, 83521, 104976, 130321, 160000, 194481, 234256, 279841, 314928, 320000, 390625, 456976, 614656, 707281, 810000, 923521, 1185921, 1229312, 1336336, 1500625, 1679616

Offset: 1

David James Sycamore, Apr 29 2024

nonn

In other words, numbers m such that if p^k is the greatest power of any prime p which divides m, then k is a term > 1 in A001694.
Subsequence of A001694 (since all prime exponents are > 1).
Compare with A361177, of which this is a subsequence (see Formula).
Distinct from A277562; A277652(26) = 331776 = 2^12 * 3^4 is not in this sequence. - Michael De Vlieger, Apr 30 2024
1 and 41472 are two terms here that are not in A277562. - David A. Corneth, Apr 30 2024

			16 = 2^4 and 4 = A001694(2) is a powerful number.
a(7) = 1296 = 2^4*3^4.
a(12) = 19683 = 3^9 (9 = A001694(4) is a powerful number).

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1580 terms from Michael De Vlieger)

Intersection of A001694 and A361177.

Subsequence of A036967.

nn = 2^21; f[x_] := f[x] = Times @@ FactorInteger[x][[All, 1]]; Select[Union@ Flatten@ Table[a^7*b^6*c^5*d^4, {d, Surd[nn, 4]}, {c, Surd[nn/d^4, 5]}, {b, Surd[nn/(c^5*d^4), 6]}, {a, Surd[nn/(b^6*c^5*d^4), 7]}], AllTrue[FactorInteger[#][[All, -1]], Divisible[#, f[#]^2] &] &] (* Michael De Vlieger, Apr 29 2024 *)

isok(k) = if (ispowerful(k), my(f=factor(k)[,2]); #select(ispowerful, f) == #f); \\ Michel Marcus, Apr 30 2024

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=2} 1/p^A001694(k)) = 1.08410926642148594327... . - Amiram Eldar, May 12 2024

More terms from Michael De Vlieger, Apr 29 2024

A372841 4-full numbers that are not prime powers.

Original entry on oeis.org

1296, 2592, 3888, 5184, 7776, 10000, 10368, 11664, 15552, 20000, 20736, 23328, 31104, 34992, 38416, 40000, 41472, 46656, 50000, 50625, 62208, 69984, 76832, 80000, 82944, 93312, 100000, 104976, 124416, 139968, 151875, 153664, 160000, 165888, 186624, 194481, 200000

Offset: 1

Michael De Vlieger, May 14 2024

nonn

Numbers k such that rad(k)^4 | k and omega(k) > 1. In other words, numbers with at least 2 distinct prime factors whose prime power factors have exponents that exceed 3.
Proper subset of the following sequences: A001694, A036966, A036967, A126706, A286708, A372695.
Smallest term k with omega(k) = m is k = A002110(m)^4.

			Table of smallest 12 terms:
   n      a(n)
  -----------------------
   1     1296 = 2^4 * 3^4
   2     2592 = 2^5 * 3^4
   3     3888 = 2^4 * 3^5
   4     5184 = 2^6 * 3^4
   5     7776 = 2^5 * 3^5
   6    10000 = 2^4 * 5^4
   7    10368 = 2^7 * 3^4
   8    11664 = 2^4 * 3^6
   9    15552 = 2^6 * 3^5
  10    20000 = 2^5 * 5^4
  11    20736 = 2^8 * 3^4
  12    23328 = 2^5 * 3^6

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

Cf. A001694, A007947, A024619, A036966, A036967, A126706, A286708, A372695.

With[{nn = 200000}, Rest@ Select[Union@ Flatten@ Table[a^7 * b^6 * c^5 * d^4, {d, Surd[nn, 4]}, {c, Surd[nn/(d^4), 5]}, {b, Surd[nn/(c^5 * d^4), 6]}, {a, Surd[nn/(b^6 * c^5 * d^4), 7]}], Not@*PrimePowerQ]]

from math import gcd
from sympy import primepi, integer_nthroot, factorint
def A372841(n):
    def f(x):
        c = n+x+1+sum(primepi(integer_nthroot(x, k)[0]) for k in range(4, x.bit_length()))
        for u in range(1,integer_nthroot(x,7)[0]+1):
            if all(d<=1 for d in factorint(u).values()):
                for w in range(1,integer_nthroot(a:=x//u**7,6)[0]+1):
                    if gcd(w,u)==1 and all(d<=1 for d in factorint(w).values()):
                        for y in range(1,integer_nthroot(z:=a//w**6,5)[0]+1):
                            if gcd(w,y)==1 and gcd(u,y)==1 and all(d<=1 for d in factorint(y).values()):
                                c -= integer_nthroot(z//y**5,4)[0]
        return c
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    return bisection(f,n,n) # Chai Wah Wu, Sep 10 2024

Intersection of A036967 and A024619.

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p^3*(p-1))) - Sum_{p prime} 1/(p^3*(p-1)) - 1 = 0.0026996042121456100761... . - Amiram Eldar, May 17 2024

cp's OEIS Frontend

A069493 6-full numbers: if p divides n then so does p^6.

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A258569 Smallest prime factors of 4-full numbers, a(1)=1.

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A385049 The sum of the unitary divisors of n that are biquadratefree numbers (A046100).

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A076468 Perfect powers m^k where k >= 4.

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A377022 Numbers whose prime factorization has exponents that have no digit 1 in their factorial-base representation (A255411).

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A297075 Lexicographically earliest sequence of distinct positive numbers such that the prime factorizations of two consecutive terms never share a prime exponent >= 1.

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A358250 Numbers whose square has a number of divisors coprime to 210.

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