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A279061 Number of divisors of n of the form 7*k + 1. 1
0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 3, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Möebius transform is a period-7 sequence {1, 0, 0, 0, 0, 0, 0, ...}.

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: Sum_{k>=1} x^k/(1 - x^(7*k)).

G.f.: Sum_{k>=0} x^(7*k+1)/(1 - x^(7*k+1)).

EXAMPLE

a(8) = 2 because 8 has 4 divisors {1,2,4,8} among which 2 divisors {1,8} are of the form 7*k + 1.

MAPLE

N:= 200: # to get a(0)..a(N)

V:= Vector(N):

for k from 1 to N do

  R:= [seq(i, i=k..N, 7*k)];

  V[R]:= map(`+`, V[R], 1);

od:

0, seq(V[i], i=1..N); # Robert Israel, Dec 05 2016

MATHEMATICA

nmax = 120; CoefficientList[Series[Sum[x^k/(1 - x^(7 k)), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 120; CoefficientList[Series[Sum[x^(7 k + 1)/(1 - x^(7 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x]

PROG

(PARI) concat([0], Vec(sum(k=1, 100, x^k / (1 - x^(7*k))) + O(x^101))) \\ Indranil Ghosh, Mar 29 2017

CROSSREFS

Cf. A001227, A001817, A001826, A001876, A188169.

Sequence in context: A187447 A146292 A139039 * A206491 A122172 A030613

Adjacent sequences:  A279058 A279059 A279060 * A279062 A279063 A279064

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Dec 05 2016

STATUS

approved

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Last modified September 29 06:29 EDT 2020. Contains 337425 sequences. (Running on oeis4.)