A143325 -id:A143325 - cp's OEIS frontend

A000740 Number of 2n-bead balanced binary necklaces of fundamental period 2n, equivalent to reversed complement; also Dirichlet convolution of b_n=2^(n-1) with mu(n); also number of components of Mandelbrot set corresponding to Julia sets with an attractive n-cycle.

1, 1, 3, 6, 15, 27, 63, 120, 252, 495, 1023, 2010, 4095, 8127, 16365, 32640, 65535, 130788, 262143, 523770, 1048509, 2096127, 4194303, 8386440, 16777200, 33550335, 67108608, 134209530, 268435455, 536854005, 1073741823, 2147450880

Offset: 1

N. J. A. Sloane

Also number of compositions of n into relatively prime parts (that is, the gcd of all the parts is 1). Also number of subsets of {1,2,..,n} containing n and consisting of relatively prime numbers. - Vladeta Jovovic, Aug 13 2003
Also number of perfect parity patterns that have exactly n columns (see A118141). - Don Knuth, May 11 2006
a(n) is odd if and only if n is squarefree (Tim Keller). - Emeric Deutsch, Apr 27 2007
a(n) is a multiple of 3 for all n>=3 (see Problem 11161 link). - Emeric Deutsch, Aug 13 2008
Row sums of triangle A143424. - Gary W. Adamson, Aug 14 2008
a(n) is the number of monic irreducible polynomials with nonzero constant coefficient in GF(2)[x] of degree n. - Michel Marcus, Oct 30 2016
a(n) is the number of aperiodic compositions of n, the number of compositions of n with relatively prime parts, and the number of compositions of n with relatively prime run-lengths. - Gus Wiseman, Dec 21 2017

			For n=4, there are 6 compositions of n into coprime parts: <3,1>, <2,1,1>, <1,3>, <1,2,1>, <1,1,2>, and <1,1,1,1>.
From _Gus Wiseman_, Dec 19 2017: (Start)
The a(6) = 27 aperiodic compositions are:
  (11112), (11121), (11211), (12111), (21111),
  (1113), (1122), (1131), (1221), (1311), (2112), (2211), (3111),
  (114), (123), (132), (141), (213), (231), (312), (321), (411),
  (15), (24), (42), (51),
  (6).
The a(6) = 27 compositions into relatively prime parts are:
  (111111),
  (11112), (11121), (11211), (12111), (21111),
  (1113), (1122), (1131), (1212), (1221), (1311), (2112), (2121), (2211), (3111),
  (114), (123), (132), (141), (213), (231), (312), (321), (411),
  (15), (51).
The a(6) = 27 compositions with relatively prime run-lengths are:
  (11112), (11121), (11211), (12111), (21111),
  (1113), (1131), (1212), (1221), (1311), (2112), (2121), (3111),
  (114), (123), (132), (141), (213), (231), (312), (321), (411),
  (15), (24), (42), (51),
  (6).
(End)

H. O. Peitgen and P. H. Richter, The Beauty of Fractals, Springer-Verlag; contribution by A. Douady, p. 165.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Seiichi Manyama, Table of n, a(n) for n = 1..3322 (terms 1..300 from T. D. Noe)
Hunki Baek, Sejeong Bang, Dongseok Kim, and Jaeun Lee, A bijection between aperiodic palindromes and connected circulant graphs, arXiv:1412.2426 [math.CO], 2014. See Table 2.
Donald Knuth, Robin Chapman and Reiner Martin, Problem 11243, Perfect Parity Patterns, Am. Math. Monthly 115 (7) (2008) p 668, function c(n).
Emeric Deutsch and Lafayette College Problem Group, Problem 11161: Compositions without Common Factors, American Mathematical Monthly, vol. 114, No. 4, 2007, p. 363.
H. W. Gould, Binomial coefficients, the bracket function and compositions with relatively prime summands, Fib. Quart. 2(4) (1964), 241-260.
J. E. Iglesias, A formula for the number of closest packings of equal spheres having a given repeat period, Z. Krist. 155 (1981) 121-127, Table 2.
Wolfdieter Lang, Cantor's List of Real Algebraic Numbers of Heights 1 to 7, arXiv:2307.10645 [math.NT], 2023.
Nicolae Mihalache and Francois Vigneron, Factorization of the quadratic Misiurewicz-Thurston polynomials, arXiv:2506.17662 [math.DS], 2025. See p. 8.
Robert Munafo, Enumeration of Period-N Mu-Atoms
Jeffrey Shallit and N. J. A. Sloane, Correspondence 1974-1975
François Vigneron and Nicolae Mihalache, How to split a tera-polynomial, arXiv:2402.06083 [math.NA], 2024.
Index entries for sequences related to Lyndon words

Cf. A000837, A003239, A008683, A008965, A022553, A034738, A035928, A038199, A051168, A054525, A056267, A059966, A143424, A167606, A178472, A216954, A228369, A294859, A296302.
Equals A027375/2.
See A056278 for a variant.
First differences of A085945.
Column k=2 of A143325.
Row sums of A101391.

with(numtheory): a[1]:=1: a[2]:=1: for n from 3 to 32 do div:=divisors(n): a[n]:=2^(n-1)-sum(a[n/div[j]],j=2..tau(n)) od: seq(a[n],n=1..32); # Emeric Deutsch, Apr 27 2007
with(numtheory); A000740:=n-> add(mobius(n/d)*2^(d-1), d in divisors(n)); # N. J. A. Sloane, Oct 18 2012

a[n_] := Sum[ MoebiusMu[n/d]*2^(d - 1), {d, Divisors[n]}]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Feb 03 2012, after PARI *)

a(n) = sumdiv(n,d,moebius(n/d)*2^(d-1))

from sympy import mobius, divisors
def a(n): return sum([mobius(n // d) * 2**(d - 1) for d in divisors(n)])
[a(n) for n in range(1, 101)]  # Indranil Ghosh, Jun 28 2017

a(n) = Sum_{d|n} mu(n/d)*2^(d-1), Mobius transform of A011782. Furthermore, Sum_{d|n} a(d) = 2^(n-1).
a(n) = A027375(n)/2 = A038199(n)/2.
a(n) = Sum_{k=0..n} A051168(n,k)*k. - Max Alekseyev, Apr 09 2013
Recurrence relation: a(n) = 2^(n-1) - Sum_{d|n,d>1} a(n/d). (Lafayette College Problem Group; see the Maple program and Iglesias eq (6)). - Emeric Deutsch, Apr 27 2007
G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 2*x^k). - Ilya Gutkovskiy, Oct 24 2018
G.f. satisfies Sum_{n>=1} A( (x/(1 + 2*x))^n ) = x. - Paul D. Hanna, Apr 02 2025

Connection with Mandelbrot set discovered by Warren D. Smith and proved by Robert Munafo, Feb 06 2000

Ambiguous term a(0) removed by Max Alekseyev, Jan 02 2012

A143324 Table T(n,k) by antidiagonals. T(n,k) is the number of length n primitive (=aperiodic or period n) k-ary words (n,k >= 1).

Original entry on oeis.org

1, 2, 0, 3, 2, 0, 4, 6, 6, 0, 5, 12, 24, 12, 0, 6, 20, 60, 72, 30, 0, 7, 30, 120, 240, 240, 54, 0, 8, 42, 210, 600, 1020, 696, 126, 0, 9, 56, 336, 1260, 3120, 4020, 2184, 240, 0, 10, 72, 504, 2352, 7770, 15480, 16380, 6480, 504, 0, 11, 90, 720, 4032, 16800, 46410, 78120, 65280, 19656, 990, 0

Offset: 1

Alois P. Heinz, Aug 07 2008

Column k is Dirichlet convolution of mu(n) with k^n.

The coefficients of the polynomial of row n are given by the n-th row of triangle A054525; for example row 4 has polynomial -k^2+k^4.

			T(2,3)=6, because there are 6 primitive words of length 2 over 3-letter alphabet {a,b,c}: ab, ac, ba, bc, ca, cb; note that the non-primitive words aa, bb and cc don't belong to the list; secondly note that the words in the list need not be Lyndon words, for example ba can be derived from ab by a cyclic rotation of the positions.
Table begins:
  1,  2,   3,    4,    5, ...
  0,  2,   6,   12,   20, ...
  0,  6,  24,   60,  120, ...
  0, 12,  72,  240,  600, ...
  0, 30, 240, 1020, 3120, ...

Alois P. Heinz, Antidiagonals n = 1..141, flattened
C. J. Smyth, A coloring proof of a generalisation of Fermat's little theorem, Amer. Math. Monthly 93, No. 6 (1986), pp. 469-471.
Lucas Vieira Barbosa, Nonclassical Temporal Correlations Under Finite-Memory Constraints, Doctoral Thesis, Univ. Wien (Austria 2024). See p. 35.
Index entries for sequences related to Lyndon words

Columns k=1-10 give: A000007(n-1), A027375, A054718, A054719, A054720, A054721, A218124, A218125, A218126, A218127.
Rows n=1-10 give: A000027, A002378(k-1), A007531(k+1), A047928(k+1), A061167, A218130, A133499, A218131, A218132, A218133.
Main diagonal gives A252764.
Cf. A074650, A143325, A008683, A054525.

with(numtheory): f0:= proc(n) option remember; unapply(k^n-add(f0(d)(k), d=divisors(n)minus{n}), k) end; T:= (n,k)-> f0(n)(k); seq(seq(T(n, 1+d-n), n=1..d), d=1..12);

f0[n_] := f0[n] = Function [k, k^n - Sum[f0[d][k], {d, Complement[Divisors[n], {n}]}]]; t[n_, k_] := f0[n][k]; Table[Table[t[n, 1 + d - n], {n, 1, d}], {d, 1, 12}] // Flatten (* Jean-François Alcover, Dec 12 2013, translated from Maple *)

T(n,k) = Sum_{d|n} k^d * mu(n/d).

T(n,k) = k^n - Sum_{d

T(n,k) = A143325(n,k) * k.

T(n,k) = A074650(n,k) * n.

So Sum_{d|n} k^d * mu(n/d) == 0 (mod n), this is a generalization of Fermat's little theorem k^p - k == 0 (mod p) for primes p to an arbitrary modulus n (see the Smyth link). - Franz Vrabec, Feb 09 2021

A143327 Table T(n,k) by antidiagonals. T(n,k) is the number of primitive (=aperiodic) k-ary words (n,k >= 1) with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 11, 11, 1, 1, 5, 19, 35, 26, 1, 1, 6, 29, 79, 115, 53, 1, 1, 7, 41, 149, 334, 347, 116, 1, 1, 8, 55, 251, 773, 1339, 1075, 236, 1, 1, 9, 71, 391, 1546, 3869, 5434, 3235, 488, 1, 1, 10, 89, 575, 2791, 9281, 19493, 21754, 9787, 983, 1, 1, 11

Offset: 1

Alois P. Heinz, Aug 07 2008

The coefficients of the polynomial of row n are given by the n-th row of triangle A134541; for example row 4 has polynomial -1+k^2+k^3.

			T(3,3) = 11, because 11 words of length <=3 over 3-letter alphabet {a,b,c} are primitive and earlier than others derived by cyclic shifts of the alphabet: a, ab, ac, aab, aac, aba, abb, abc, aca, acb, acc.
Table begins:
  1,   1,    1,     1,     1,      1,      1,       1, ...
  1,   2,    3,     4,     5,      6,      7,       8, ...
  1,   5,   11,    19,    29,     41,     55,      71, ...
  1,  11,   35,    79,   149,    251,    391,     575, ...
  1,  26,  115,   334,   773,   1546,   2791,    4670, ...
  1,  53,  347,  1339,  3869,   9281,  19543,   37367, ...
  1, 116, 1075,  5434, 19493,  55936, 137191,  299510, ...
  1, 236, 3235, 21754, 97493, 335656, 960391, 2396150, ...

Alois P. Heinz, Antidiagonals n = 1..141, flattened
Index entries for sequences related to Lyndon words

Columns k=1-10 give: A000012, A085945, A320087, A320088, A320089, A320090, A320091, A320092, A320093, A320094.
Rows n=1-4 give: A000012, A000027, A028387, A003777.
Main diagonal gives A320095.
Cf. A143325, A143326, A134541, A008683.

with(numtheory):
f1:= proc (n) option remember; unapply(k^(n-1)
        -add(f1(d)(k), d=divisors(n) minus {n}), k)
     end:
g1:= proc(n) option remember; unapply(add(f1(j)(x), j=1..n), x) end:
T:= (n, k)-> g1(n)(k):
seq(seq(T(n, 1+d-n), n=1..d), d=1..12);

t[n_, k_] := Sum[k^(d-1)*MoebiusMu[j/d], {j, 1, n}, {d, Divisors[j]}]; Table[t[n-k+1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Dec 13 2013 *)

T(n,k) = Sum_{j=1..n} Sum_{d|j} k^(d-1) * mu(j/d).
T(n,k) = Sum_{j=1..n} A143325(j,k).
T(n,k) = A143326(n,k) / k.

A075147 Number of Lyndon words (aperiodic necklaces) with n beads of n colors.

Original entry on oeis.org

1, 1, 8, 60, 624, 7735, 117648, 2096640, 43046640, 999989991, 25937424600, 743008120140, 23298085122480, 793714765724595, 29192926025339776, 1152921504338411520, 48661191875666868480, 2185911559727674682148, 104127350297911241532840, 5242879999999487999992020

Offset: 1

Christian G. Bower, Sep 04 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..350
Index entries for sequences related to Lyndon words.

Main diagonal of A074650 and A143325.

Cf. A000169, A008683, A306173.

with(numtheory):
a:= n-> add(n^d *mobius(n/d), d=divisors(n))/n:
seq(a(n), n=1..25);  # Alois P. Heinz, Dec 21 2014

Table[Total@Map[ MoebiusMu[#1] n^(n/#1 - 1) &, Divisors[n]], {n, 20}] (* Olivier Gérard, Aug 05 2016 *)

a(n) = sumdiv(n, d, moebius(n/d) * n^d) / n; \\ Amiram Eldar, May 29 2025

a(n) = (1/n) * Sum_{d|n} mu(n/d)*n^d.
Asymptotic to n^(n-1) = A000169(n).
a(n) is the n-th term of the inverse Euler transform of j-> n^j. - Alois P. Heinz, Jun 23 2018
a(n) = [x^n] Sum_{k>=1} mu(k)*log(1/(1 - n*x^k))/k. - Ilya Gutkovskiy, May 20 2019

A034741 Dirichlet convolution of mu(n) with 3^(n-1).

Original entry on oeis.org

1, 2, 8, 24, 80, 232, 728, 2160, 6552, 19600, 59048, 176880, 531440, 1593592, 4782880, 14346720, 43046720, 129133368, 387420488, 1162241760, 3486783664, 10460294152, 31381059608, 94142999520, 282429536400, 847288078000, 2541865821768, 7625595890640, 22876792454960

Offset: 1

Erich Friedman

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..2096

Column k=3 of A143325.
First differences of A320087.
Cf. A054718.

nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k] * x^k / (1 - 3*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)

a(n) = sumdiv(n,d, moebius(d) * 3^(n/d-1) ); \\ Joerg Arndt, Apr 14 2013

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 3*x^k). - Ilya Gutkovskiy, Oct 25 2018

a(n) ~ 3^(n-1). - Vaclav Kotesovec, Sep 11 2019

A295505 a(n) = Sum_{d|n} mu(n/d)*4^(d-1).

Original entry on oeis.org

1, 3, 15, 60, 255, 1005, 4095, 16320, 65520, 261885, 1048575, 4193220, 16777215, 67104765, 268435185, 1073725440, 4294967295, 17179802640, 68719476735, 274877644740, 1099511623665, 4398045462525, 17592186044415, 70368739967040, 281474976710400

Offset: 1

Seiichi Manyama, Nov 23 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..1661

Sum_{d|n} mu(n/d)*k^(d-1): A000740 (k=2), A034741 (k=3), this sequence (k=4), A295506 (k=5).
Column k=4 of A143325.
First differences of A320088.
Cf. A054719.

Table[Sum[MoebiusMu[n/d]4^(d-1),{d,Divisors[n]}],{n,30}] (* Harvey P. Dale, Nov 08 2020 *)
nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k] * x^k / (1 - 4*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)

{a(n) = sumdiv(n, d, moebius(n/d)*4^(d-1))}

a(n) = A054719(n)/4 for n > 0.

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 4*x^k). - Ilya Gutkovskiy, Oct 25 2018

A295506 a(n) = Sum_{d|n} mu(n/d)*5^(d-1).

Original entry on oeis.org

1, 4, 24, 120, 624, 3096, 15624, 78000, 390600, 1952496, 9765624, 48824880, 244140624, 1220687496, 6103514976, 30517500000, 152587890624, 762939059400, 3814697265624, 19073484374880, 95367431624976, 476837148437496, 2384185791015624, 11920928906172000

Offset: 1

Seiichi Manyama, Nov 23 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..1431

Sum_{d|n} mu(n/d)*k^(d-1): A000740 (k=2), A034741 (k=3), A295505 (k=4), this sequence (k=5).
Column k=5 of A143325.
First differences of A320089.
Cf. A054720.

nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k] * x^k / (1 - 5*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)

{a(n) = sumdiv(n, d, moebius(n/d)*5^(d-1))}

a(n) = A054720(n)/5 for n > 0.

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 5*x^k). - Ilya Gutkovskiy, Oct 25 2018

A252764 Number of length n primitive (=aperiodic or period n) n-ary words.

Original entry on oeis.org

1, 2, 24, 240, 3120, 46410, 823536, 16773120, 387419760, 9999899910, 285311670600, 8916097441680, 302875106592240, 11112006720144330, 437893890380096640, 18446744069414584320, 827240261886336764160, 39346408075098144278664, 1978419655660313589123960

Offset: 1

Alois P. Heinz, Dec 21 2014

nonn

			a(3) = 24 because there are 24 primitive words of length 3 over 3-letter alphabet {a,b,c}: aab, aac, aba, abb, abc, aca, acb, acc, baa, bab, bac, bba, bbc, bca, bcb, bcc, caa, cab, cac, cba, cbb, cbc, cca, ccb.

Alois P. Heinz, Table of n, a(n) for n = 1..350

Main diagonal of A143324.

Cf. A008683, A074650, A075147, A143324, A143325.

with(numtheory):
a:= n-> add(n^d *mobius(n/d), d=divisors(n)):
seq(a(n), n=1..25);

a[n_] := DivisorSum[n, n^# * MoebiusMu[n/#]& ];
Array[a, 25] (* Jean-François Alcover, Mar 24 2017, translated from Maple *)

a(n) = Sum_{d|n} n^d * mu(n/d), mu = A008683.
a(n) = A075147(n)*n.
a(n) = A074650(n,n) * n.
a(n) = A143325(n,n) * n.
a(n) = A143324(n,n).

A320071 Number of length n primitive (=aperiodic or period n) 6-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

Original entry on oeis.org

1, 5, 35, 210, 1295, 7735, 46655, 279720, 1679580, 10076395, 60466175, 362789070, 2176782335, 13060647355, 78364162765, 470184704640, 2821109907455, 16926657757380, 101559956668415, 609359729932590, 3656158440016285, 21936950579911675, 131621703842267135

Offset: 1

Alois P. Heinz, Oct 05 2018

nonn

Dirichlet convolution of mu(n) with 6^(n-1).

Alois P. Heinz, Table of n, a(n) for n = 1..1286

Column k=6 of A143325.
First differences of A320090.
Cf. A008683, A074650, A143324.

a:= n-> add(`if`(d=n, 6^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);

nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k] * x^k / (1 - 6*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)

a(n) = Sum_{d|n} 6^(d-1) * mu(n/d).

a(n) = 6^(n-1) - Sum_{d

a(n) = A143325(n,6).

a(n) = A074650(n,6) * n/6.

a(n) = A143324(n,6) / 6.

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 6*x^k). - Ilya Gutkovskiy, Oct 25 2018

A320072 Number of length n primitive (=aperiodic or period n) 7-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

Original entry on oeis.org

1, 6, 48, 336, 2400, 16752, 117648, 823200, 5764752, 40351200, 282475248, 1977309600, 13841287200, 96888892752, 678223070400, 4747560686400, 33232930569600, 232630508205648, 1628413597910448, 11398895145019200, 79792266297494304, 558545863800808752

Offset: 1

Alois P. Heinz, Oct 05 2018

nonn

Dirichlet convolution of mu(n) with 7^(n-1).

Alois P. Heinz, Table of n, a(n) for n = 1..1184

Column k=7 of A143325.
First differences of A320091.
Cf. A008683, A074650, A143324.

a:= n-> add(`if`(d=n, 7^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);

a(n) = Sum_{d|n} 7^(d-1) * mu(n/d).

a(n) = 7^(n-1) - Sum_{d

a(n) = A143325(n,7).

a(n) = A074650(n,7) * n/7.

a(n) = A143324(n,7) / 7.

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 7*x^k). - Ilya Gutkovskiy, Oct 25 2018

Showing 1-10 of 23 results. Next

cp's OEIS Frontend

A000740 Number of 2n-bead balanced binary necklaces of fundamental period 2n, equivalent to reversed complement; also Dirichlet convolution of b_n=2^(n-1) with mu(n); also number of components of Mandelbrot set corresponding to Julia sets with an attractive n-cycle.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

Extensions

A143324 Table T(n,k) by antidiagonals. T(n,k) is the number of length n primitive (=aperiodic or period n) k-ary words (n,k >= 1).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A143327 Table T(n,k) by antidiagonals. T(n,k) is the number of primitive (=aperiodic) k-ary words (n,k >= 1) with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A075147 Number of Lyndon words (aperiodic necklaces) with n beads of n colors.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A034741 Dirichlet convolution of mu(n) with 3^(n-1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A295505 a(n) = Sum_{d|n} mu(n/d)*4^(d-1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A295506 a(n) = Sum_{d|n} mu(n/d)*5^(d-1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica