A007947 -id:A007947 - cp's OEIS frontend

A081770 Numbers twice their squarefree kernel (A007947).

4, 12, 20, 28, 44, 52, 60, 68, 76, 84, 92, 116, 124, 132, 140, 148, 156, 164, 172, 188, 204, 212, 220, 228, 236, 244, 260, 268, 276, 284, 292, 308, 316, 332, 340, 348, 356, 364, 372, 380, 388, 404, 412, 420, 428, 436, 444, 452, 460, 476, 492, 508, 516, 524

Offset: 1

Reinhard Zumkeller, Apr 10 2003

From Amiram Eldar, Nov 02 2020: (Start)
Numbers k such that A280292(k) = 2.
The asymptotic density of this sequence is 1/Pi^2 (A092742). (End)

			84=2*2*3*7=2*(2*3*7)=2*rad(84), therefore 84 is a term.

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

Cf. A001414, A005117, A007947, A008472, A008966, A013929, A039956, A056911, A092742, A280292.

Subsequence of A017113.

a081770 n = a081770_list !! (n-1)
a081770_list = filter ((== 1) . a008966 . (`div` 4)) a017113_list
-- Reinhard Zumkeller, Jul 13 2013

4 * Select[Range[1, 100, 2], SquareFreeQ] (* Amiram Eldar, Nov 02 2020 *)

is(n)=n%8==4 && issquarefree(n/4) \\ Charles R Greathouse IV, Jul 09 2013

a(n) = 2*A039956(n) = 4*A056911(n).

A326144 a(n) = gcd(A066503(n), A326143(n)) = gcd(n - A007947(n), sigma(n) - A007947(n) - n).

Original entry on oeis.org

1, 1, 2, 1, 4, 0, 6, 1, 1, 2, 10, 2, 12, 4, 6, 1, 16, 3, 18, 2, 10, 8, 22, 6, 1, 10, 2, 14, 28, 12, 30, 1, 18, 14, 22, 1, 36, 16, 22, 10, 40, 12, 42, 2, 6, 20, 46, 14, 1, 1, 30, 2, 52, 12, 38, 2, 34, 26, 58, 6, 60, 28, 2, 1, 46, 12, 66, 2, 42, 4, 70, 3, 72, 34, 2, 2, 58, 12, 78, 2, 1, 38, 82, 14, 62, 40, 54, 2, 88, 6, 70, 2

Offset: 1

Antti Karttunen, Jun 09 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A000203, A007947, A066503, A326142, A326143, A326145.

Cf. also A009194, A325385, A325813, A325975, A326046, A326047, A326048, A326056, A326057, A326060, A326062, A326129, A326130, A326140.

rad[n_] := Times @@ (First /@ FactorInteger@n);
a[n_] := GCD[n - rad[n], DivisorSigma[1, n] - rad[n] - n];
Array[a, 100] (* Jean-François Alcover, Dec 01 2021 *)

A007947(n) = factorback(factorint(n)[, 1]);
A066503(n) = (n - A007947(n));
A326143(n) = (sigma(n)-A007947(n)-n);
A326144(n) = gcd(A066503(n), A326143(n));

a(n) = gcd(A066503(n), A326143(n)) = gcd(n-A007947(n), A000203(n)-A007947(n)-n).

A028235 If n = Product (p_j^k_j), a(n) = numerator of Sum 1/p_j (the denominator of this sum is A007947).

Original entry on oeis.org

0, 1, 1, 1, 1, 5, 1, 1, 1, 7, 1, 5, 1, 9, 8, 1, 1, 5, 1, 7, 10, 13, 1, 5, 1, 15, 1, 9, 1, 31, 1, 1, 14, 19, 12, 5, 1, 21, 16, 7, 1, 41, 1, 13, 8, 25, 1, 5, 1, 7, 20, 15, 1, 5, 16, 9, 22, 31, 1, 31, 1, 33, 10, 1, 18, 61, 1, 19, 26, 59, 1, 5, 1, 39, 8, 21, 18, 71, 1, 7, 1, 43, 1, 41, 22, 45, 32

Offset: 1

N. J. A. Sloane

For n=1, the empty sum = 0 = 0/1 = a(1)/A007947(1), thus a(1) should be 0. - Antti Karttunen, Mar 04 2018

			Fractions begin with 0, 1/2, 1/3, 1/2, 1/5, 5/6, 1/7, 1/2, 1/3, 7/10, 1/11, 5/6, ...

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A007947 (denominators), A003415, A069359, A085548, A379967.

a[1] = 0; a[n_] := 1/FactorInteger[n][[All, 1]] // Total // Numerator;
Array[a, 100] (* Jean-François Alcover, May 08 2019 *)

A028235(n) = numerator(vecsum(apply(p->(1/p), factor(n)[, 1]))); \\ Antti Karttunen, Mar 04 2018

Fraction is additive with a(p^e) = 1/p.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A007947(k) = Sum_{p prime} 1/p^2 = 0.452247... (A085548). - Amiram Eldar, Sep 29 2023
a(n) = A003415(A007947(n)) = A069359(A007947(n)). - Antti Karttunen, Jan 22 2025

More terms from Erich Friedman.

Term a(1) changed to 0 by Antti Karttunen, Mar 04 2018

A369609 Irregular triangle read by rows where row n lists k <= n such that A007947(k) = A007947(n).

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 7, 2, 4, 8, 3, 9, 10, 11, 6, 12, 13, 14, 15, 2, 4, 8, 16, 17, 6, 12, 18, 19, 10, 20, 21, 22, 23, 6, 12, 18, 24, 5, 25, 26, 3, 9, 27, 14, 28, 29, 30, 31, 2, 4, 8, 16, 32, 33, 34, 35, 6, 12, 18, 24, 36, 37, 38, 39, 10, 20, 40, 41, 42, 43, 22, 44

Offset: 1

Michael De Vlieger, May 09 2024

Differs from A284318 after 27 terms.
Let rad(x) = A007947(x).
Let T(n,k) be the k-th term of row n in this sequence.
Define S(n,k) to be the k-th term in row n of A162306.
T(n,k) = rad(n) * S(n,k), k <= A008479(n).
The number n appears as the last term in row n.

			First rows of the triangle:
  1;
  2;
  3;
  2, 4;
  5;
  6;
  7;
  2, 4, 8;
  3, 9;
  10;
  11;
  6, 12;
  13;
  14;
  15;
  2, 4, 8, 16;
  17;
  6, 12, 18;
  etc.

Michael De Vlieger, Table of n, a(n) for n = 1..12946 (rows n = 1..5000, flattened)
Michael De Vlieger, Fast Mathematica programs that construct A008479, A010846, A162306, and A369609

Cf. A007947, A008479, A162306, A284318.

f[x_] := f[x] = Times @@ FactorInteger[x][[All, 1]]; Flatten@ Table[r = f[n]; Select[Range[n], f[#] == r &], {n, 44}]

rad(n) = factorback(factorint(n)[, 1]); \\ A007947
row(n) = my(r=rad(n)); select(x->(rad(x) == r), [1..n]); \\ Michel Marcus, May 11 2024

Row n of this sequence contains row n of A284318.
Length of row n is A008479(n).
For squarefree n, row n = {n}.
For prime power n = p^m, row n = { p^j : j = 1..m }.

A284457 Square array whose rows list numbers with the same squarefree kernel (A007947): Transpose of A284311.

Original entry on oeis.org

2, 4, 3, 8, 9, 5, 16, 27, 25, 6, 32, 81, 125, 12, 7, 64, 243, 625, 18, 49, 10, 128, 729, 3125, 24, 343, 20, 11, 256, 2187, 15625, 36, 2401, 40, 121, 13, 512, 6561, 78125, 48, 16807, 50, 1331, 169, 14, 1024, 19683, 390625, 54, 117649, 80, 14641, 2197, 28, 15

Offset: 1

Bob Selcoe, Mar 27 2017

The first column contains the squarefree numbers A005117; each row lists all numbers having the same prime divisors. If T[m,1] is prime then the row contains the powers of that prime. Yields A182944 if only these rows with prime powers (A000961) are kept. - M. F. Hasler, Mar 27 2017

See A284311 for further details.

			Array starts:
    2    4     8     16      32      64      128
    3    9    27     81     243     729     2187
    5   25   125    625    3125   15625    78125
    6   12    18     24      36      48       54
    7   49   343   2401   16807  117649   823543
   10   20    40     50      80     100      160
   ...
Row 6 is: T[1,6] = 2*5; T[2,6] = 2^2*5; T[3,6] = 2^3*5; T[4,6] = 2*5^2; T[5,6] = 2^4*5, etc.

Alois P. Heinz, Antidiagonals n = 1..141, flattened

Cf. A284311, A005117, A007947, A065642, A182944.

Cf. A008479 (index of the column where n is located), A285329 (of the row).

f[n_, k_: 1] := Block[{c = 0, sgn = Sign[k], sf}, sf = n + sgn; While[c < Abs@ k, While[! SquareFreeQ@ sf, If[sgn < 0, sf--, sf++]]; If[sgn < 0, sf--, sf++]; c++]; sf + If[sgn < 0, 1, -1]] (* after Robert G. Wilson v at A005117 *); T[n_, k_] := T[n, k] = Which[And[n == 1, k == 1], 2, k == 1, f@ T[n - 1, k], PrimeQ@ T[n, 1], T[n, 1]^k, True, Module[{j = T[n, k - 1]/T[n, 1] + 1}, While[PowerMod[T[n, 1], j, j] != 0, j++]; j T[n, 1]]]; Table[T[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten

A284457(m,n)={for(a=2,m^2+1,(core(a)!=a||m--)&&next;m=factor(a)[,1]; for(k=1,9e9,factor(k*a)[,1]==m&&!n--&&return(k*a)))} \\ M. F. Hasler, Mar 27 2017

(define (A284457 n) (A284311bi (A004736 n) (A002260 n))) ;; For A284311bi, see A284311. - Antti Karttunen, Apr 17 2017

From Antti Karttunen, Apr 17 2017: (Start)
A(n,1) = A005117(1+n), A(n,k) = A065642(A(n,k-1)). [A "dispersion" of A065642.]
A(A285329(n), A008479(n)) = n for all n >= 2.(End)

Edited by M. F. Hasler, Mar 27 2017

A322591 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 for odd primes, and A007947(n) for any other number.

Original entry on oeis.org

1, 2, 3, 2, 3, 4, 3, 2, 5, 6, 3, 4, 3, 7, 8, 2, 3, 4, 3, 6, 9, 10, 3, 4, 11, 12, 5, 7, 3, 13, 3, 2, 14, 15, 16, 4, 3, 17, 18, 6, 3, 19, 3, 10, 8, 20, 3, 4, 21, 6, 22, 12, 3, 4, 23, 7, 24, 25, 3, 13, 3, 26, 9, 2, 27, 28, 3, 15, 29, 30, 3, 4, 3, 31, 8, 17, 32, 33, 3, 6, 5, 34, 3, 19, 35, 36, 37, 10, 3, 13, 38, 20, 39, 40, 41, 4, 3, 7, 14, 6, 3, 42, 3, 12, 43

Offset: 1

Antti Karttunen, Dec 18 2018

nonn

For all i, j:
  a(i) = a(j) => A066086(i) = A066086(j),
  a(i) = a(j) => A322354(i) = A322354(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A007947, A305801, A322587, A322588, A322589, A322590, A322592.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A007947(n) = factorback(factorint(n)[, 1]);
Aux322591(n) = if((n>2)&&isprime(n),0,A007947(n));
v322591 = rgs_transform(vector(up_to, n, Aux322591(n)));
A322591(n) = v322591[n];

A376248 Irregular triangle where row n lists m such that rad(m) | n and bigomega(m) <= bigomega(n), where rad = A007947 and bigomega = A001222.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 3, 4, 6, 9, 1, 7, 1, 2, 4, 8, 1, 3, 9, 1, 2, 4, 5, 10, 25, 1, 11, 1, 2, 3, 4, 6, 8, 9, 12, 18, 27, 1, 13, 1, 2, 4, 7, 14, 49, 1, 3, 5, 9, 15, 25, 1, 2, 4, 8, 16, 1, 17, 1, 2, 3, 4, 6, 8, 9, 12, 18, 27, 1, 19, 1, 2, 4, 5, 8, 10, 20, 25, 50, 125

Offset: 1

Michael De Vlieger, Oct 09 2024

Analogous to A162306 regarding m such that rad(m) | n, but instead of taking m <= n, we take m such that bigomega(m) <= bigomega(n).
Row n is a finite set of products of prime power factors p^k (i.e., p^k | n) such that Sum_{p|n} k <= bigomega(n).
For prime power n = p^k, k >= 0 (i.e., n in A000961), row p^k of this sequence is the same as row p^k of A027750 and A162306. Therefore, for prime p, row p of this sequence is the same as row p of A027750 and A162306: {1, p}.
For n in A024619, row n of this sequence does not match row n of A162306, since the former contains gpf(n)^bigomega(n) = A006530(n)^A001222(n), which is larger than n.

			Triangle begins:
   n    row n of this sequence:
  -------------------------------------------
   1:   1;
   2:   1,  2;
   3:   1,  3;
   4:   1,  2   4;
   5:   1,  5;
   6:   1,  2,  3,  4,  6,  9;
   7:   1,  7;
   8:   1,  2,  4,  8;
   9:   1,  3,  9;
  10:   1,  2,  4,  5, 10, 25;
  11:   1, 11;
  12:   1,  2,  3,  4,  6,  8, 9, 12, 18, 27;
        ...
Row n = 10 of this sequence, presented according to 2^k, k = 0..bigomega(n) by columns, 5^i, i = 0..bigomega(n) by rows, showing terms m > n with an asterisk. The remaining m and the parenthetic 8 are in row 10 of A162306:
   1   2   4  (8)
   5  10
  25*
Row n = 12 of this sequence, presented according to 2^k, k = 0..bigomega(n) by columns, 3^i, i = 0..bigomega(n) by rows, showing terms m > n with an asterisk. The remaining m are in row 12 of A162306:
   1   2   4   8
   3   6  12
   9  18*
  27*

Michael De Vlieger, Table of n, a(n) for n = 1..17475 (rows n = 1..1000, flattened)
Michael De Vlieger, Log log scatterplot of rows n = 1..2^16 of this sequence, flattened, (3153752 terms).

Cf. A000961, A001221, A001222, A006530, A007947, A010846, A024619, A027750, A162306, A376567.

Table[Clear[p]; MapIndexed[Set[p[First[#2]], #1] &, FactorInteger[n][[All, 1]]]; k = PrimeOmega[n]; w = PrimeNu[n]; Union@ Map[Times @@ MapIndexed[p[First[#2]]^#1 &, #] &, Select[Tuples[Range[0, k], w], Total[#] <= k &] ], {n, 120}]

Row n of this sequence is { m : rad(m) | n, bigomega(m) <= bigomega(n) }.

A376567(n) = binomial(bigomega(n) + omega(n)) = Length of row n, where omega = A001221.

A071773 a(n) = gcd(rad(n), n/rad(n)), where rad(n) = A007947(n) is the squarefree kernel of n.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 5, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 7, 5, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 5, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 7, 3, 10, 1, 1, 1, 2

Offset: 1

Reinhard Zumkeller, Jun 24 2002

n is squarefree iff a(n)=1.
Product of primes dividing n more than once. - Charles R Greathouse IV, Aug 08 2013
Squarefree kernel of the square part of n. - Peter Munn, Jun 12 2020

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)
Eric Weisstein's World of Mathematics, Squarefree.

Cf. A003415, A003557, A005117, A007947, A007948, A008833, A057521, A166486 (parity of terms), A359433 (Dirichlet inverse).

Cf. A065464.

Table[With[{r = Apply[Times, FactorInteger[n][[All, 1]]]}, GCD[r, n/r]], {n, 104}] (* Michael De Vlieger, Aug 20 2017 *)

a(n)=my(f=factor(n));prod(i=1,#f~,f[i,1]^(f[i,2]>1)) \\ Charles R Greathouse IV, Aug 08 2013

;; With memoization-macro definec.
(definec (A071773 n) (if (= 1 n) n (* (if (zero? (modulo n (expt (A020639 n) 2))) (A020639 n) 1) (A071773 (A028234 n))))) ;; Antti Karttunen, Nov 28 2017

a(n) = gcd(A007947(n), A003557(n)).
Multiplicative with p^e -> p^ceiling((e-1)/e), p prime.
a(n) = rad(n/rad(n)) = A007947(A003557(n)). - Velin Yanev, Antti Karttunen, Aug 20 2017, Nov 28 2017
a(n) = A007947(A057521(n)). - Antti Karttunen, Nov 28 2017
a(n) = A007947(A008833(n)). - Peter Munn, Jun 12 2020
a(n) = gcd(A003415(n), A007947(n)). - Antti Karttunen, Jan 02 2023
Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + 1/p^(2*s-1) - 1/p^(2*s)). - Amiram Eldar, Nov 09 2023
From Vaclav Kotesovec, May 06 2025: (Start)
Let f(s) = Product_{p prime} (1 - 1/p^(2*s) + 1/p^(4*s-1) - 1/p^(4*s-2)).
Dirichlet g.f.: zeta(s) * zeta(2*s-1) * f(s).
Sum_{k=1..n} a(k) ~ f(1) * n * (log(n) + 3*gamma - 1 + f'(1)/f(1)) / 2, where
f(1) = A065464 = Product_{p prime} (1 - 2/p^2 + 1/p^3) = 0.428249505677094440218765707581823546121298513355936144031901379532123...
f'(1) = f(1) * Sum_{p prime} 2*(3*p-2)*log(p) / (p^3-2*p+1) = f(1) * 2.939073481649229666406787986900328729326669597518287791424059647447664...
and gamma is the Euler-Mascheroni constant A001620. (End)

A367417 The squarefree kernels of the exponentially odd numbers: a(n) = A007947(A268335(n)).

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 2, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 6, 26, 3, 29, 30, 31, 2, 33, 34, 35, 37, 38, 39, 10, 41, 42, 43, 46, 47, 51, 53, 6, 55, 14, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 22, 89, 91, 93, 94, 95

Offset: 1

Amiram Eldar, Nov 17 2023

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

Cf. A007947, A268335, A367406.

Cf. A013662, A065463.

s[n_] := Times @@ FactorInteger[n][[;; , 1]]; s /@ Select[Range[200], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]

b(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2]%2, f[i, 1], 0)); }
lista(kmax) = {my(b1); for(k = 1, kmax, b1 = b(k); if(b1 > 0, print1(b1, ", "))); }

a(n) = A367406(n)/A268335(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = (zeta(4)/d^2) * Product_{p prime} (1 - 1/p^2 - 1/p^4 + 1/p^5) = 1.25661974314007532208..., and d = A065463 is the asymptotic density of the exponentially odd numbers.

A078615 a(n) = rad(n)^2, where rad is the squarefree kernel of n (A007947).

Original entry on oeis.org

1, 4, 9, 4, 25, 36, 49, 4, 9, 100, 121, 36, 169, 196, 225, 4, 289, 36, 361, 100, 441, 484, 529, 36, 25, 676, 9, 196, 841, 900, 961, 4, 1089, 1156, 1225, 36, 1369, 1444, 1521, 100, 1681, 1764, 1849, 484, 225, 2116, 2209, 36, 49, 100, 2601, 676, 2809, 36, 3025, 196

Offset: 1

Reinhard Zumkeller, Dec 10 2002

It is conjectured that only 1 and 1782 satisfy a(k) = sigma(k). See Broughan link. - Michel Marcus, Feb 28 2019

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Peter Bala, GCD sum theorems. Two Multivariable Cesaro Type Identities.
K. Broughan, J.-M. De Koninck, I. Kátai, and F. Luca, On integers for which the sum of divisors is the square of the squarefree core, J. Integer Seq., 15 (2012), pp. 1-12.
Yong-Gao Chen, and Xin Tong, On a conjecture of de Koninck, Journal of Number Theory, Volume 154, September 2015, Pages 324-364. Beware of typo 1728.

Cf. A002117, A007948, A055231, A062378, A330523, A007434, A008683, A001221, A065958.

a := n -> mul(f,f=map(x->x^2,select(isprime,divisors(n))));
seq(a(n), n=1..56);  # Peter Luschny, Mar 30 2014

a[n_] := Times @@ FactorInteger[n][[All, 1]]^2; Array[a, 60] (* Jean-François Alcover, Jun 04 2019 *)

a(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i])^2 \\ Charles R Greathouse IV, Aug 06 2013

Multiplicative with a(p^e) = p^2. - Mitch Harris, May 17 2005
G.f.: Sum_{k>=1} mu(k)^2*J_2(k)*x^k/(1 - x^k), where J_2() is the Jordan function. - Ilya Gutkovskiy, Nov 06 2018
Sum_{k=1..n} a(k) ~ c * n^3, where c = (zeta(3)/3) * Product_{p prime} (1 - 1/p^2 - 1/p^3 + 1/p^4) = A002117 * A330523 / 3 = 0.214725... . - Amiram Eldar, Oct 30 2022
a(n) = Sum_{1 <= i, j <= n}  ( mobius(n/gcd(i, j, n)) )^2. - Peter Bala, Jan 28 2024
a(n) = Sum_{d|n} mu(d)^2*J_2(d), where J_2 = A007434. - Ridouane Oudra, Jul 24 2025
a(n) = (-1)^omega(n) * Sum_{d|n} mu(d)*Psi_2(d), where omega = A001221 and Psi_2 = A065958. - Ridouane Oudra, Aug 01 2025

cp's OEIS Frontend

A081770 Numbers twice their squarefree kernel (A007947).

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A326144 a(n) = gcd(A066503(n), A326143(n)) = gcd(n - A007947(n), sigma(n) - A007947(n) - n).

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A028235 If n = Product (p_j^k_j), a(n) = numerator of Sum 1/p_j (the denominator of this sum is A007947).

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A369609 Irregular triangle read by rows where row n lists k <= n such that A007947(k) = A007947(n).

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A284457 Square array whose rows list numbers with the same squarefree kernel (A007947): Transpose of A284311.

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A322591 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 for odd primes, and A007947(n) for any other number.

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A376248 Irregular triangle where row n lists m such that rad(m) | n and bigomega(m) <= bigomega(n), where rad = A007947 and bigomega = A001222.

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