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A035207 Coefficients in expansion of Dirichlet series Product_p (1 - (Kronecker(m,p) + 1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = 25. 4
1, 2, 2, 3, 1, 4, 2, 4, 3, 2, 2, 6, 2, 4, 2, 5, 2, 6, 2, 3, 4, 4, 2, 8, 1, 4, 4, 6, 2, 4, 2, 6, 4, 4, 2, 9, 2, 4, 4, 4, 2, 8, 2, 6, 3, 4, 2, 10, 3, 2, 4, 6, 2, 8, 2, 8, 4, 4, 2, 6, 2, 4, 6, 7, 2, 8, 2, 6, 4, 4, 2, 12, 2, 4, 2, 6, 4, 8, 2, 5, 5, 4, 2, 12, 2, 4, 4, 8, 2, 6, 4, 6, 4, 4, 2, 12, 2, 6, 6, 3, 2, 8, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of divisors of n not congruent to 0 mod 5.

LINKS

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

FORMULA

Multiplicative with a(5^e)=1 and a(p^e)=e+1 for p<>5.

Moebius transform is period 5 sequence [ 1, 1, 1, 1, 0, ...]. - Michael Somos, Oct 31 2006

G.f.: Sum_{k>=1} x^k*(1 + x^k + x^(2*k) + x^(3*k))/(1 - x^(5*k)). - Ilya Gutkovskiy, Sep 11 2019

a(n) = tau(5*n) - tau(n). - Ridouane Oudra, Sep 05 2020

MAPLE

for n from 1 to 500 do a := ifactors(n):s := 1:for k from 1 to nops(a[2]) do p := a[2][k][1]:e := a[2][k][2]: if p=5 then b := 1:else b := e+1:fi:s := s*b:od:printf(`%d, `, s); od:

MATHEMATICA

Table[Count[Divisors[n], _?(!Divisible[#, 5]&)], {n, 110}] (* Harvey P. Dale, Apr 08 2015 *)

f[5, e_] := 1; f[p_, e_] := e+1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 26 2020 *)

PROG

(PARI) {a(n)=if(n<1, 0, sumdiv(n, d, d%5>0))} /* Michael Somos, Oct 31 2006 */

(PARI) {a(n)=if(n<1, 0, direuler(p=2, n, 1/(1-X)/if(p==5, 1, 1-X))[n])} /* Michael Somos, Oct 31 2006 */

(MAGMA) [NumberOfDivisors(n)/Valuation(5*n, 5): n in [1..100]]; // Vincenzo Librandi, Jun 03 2019

CROSSREFS

Cf. A000005 (tau), A035191, A069733.

Cf. A116073 (sum of divisors of n not congruent to 0 mod 5).

Sequence in context: A182471 A078378 A141197 * A324829 A294618 A207507

Adjacent sequences:  A035204 A035205 A035206 * A035208 A035209 A035210

KEYWORD

nonn,mult,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Additional comments from Vladeta Jovovic, Oct 26 2001

STATUS

approved

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Last modified April 19 15:45 EDT 2021. Contains 343116 sequences. (Running on oeis4.)