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A279060 Number of divisors of n of the form 6*k + 1. 5
0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Möbius transform is the period-6 sequence {1, 0, 0, 0, 0, 0, ...}.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

FORMULA

G.f.: Sum_{k>=1} x^k/(1 - x^(6*k)).

G.f.: Sum_{k>=0} x^(6*k+1)/(1 - x^(6*k+1)).

From Antti Karttunen, Oct 03 2018: (Start)

a(n) = A320001(n) + [1 == n (mod 6)], where [ ] is the Iverson bracket, giving 1 only when n = 1 mod 6, and 0 otherwise.

a(n) = A035218(n) - A319995(n).

(End)

EXAMPLE

a(14) = 2 because 14 has 4 divisors {1,2,7,14} among which 2 divisors {1,7} are of the form 6*k + 1.

MATHEMATICA

nmax = 120; CoefficientList[Series[Sum[x^k/(1 - x^(6 k)), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 120; CoefficientList[Series[Sum[x^(6 k + 1)/(1 - x^(6 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x]

Table[Count[Divisors[n], _?(Mod[#, 6]==1&)], {n, 0, 120}] (* Harvey P. Dale, Apr 27 2018 *)

PROG

(PARI) A279060(n) = if(!n, n, sumdiv(n, d, (1==(d%6)))); \\ Antti Karttunen, Jul 09 2017

CROSSREFS

Cf. A001227, A001817, A001826, A001876, A035218, A140213, A188169, A319995, A320001.

Sequence in context: A274196 A096811 A082478 * A324119 A083382 A327168

Adjacent sequences:  A279057 A279058 A279059 * A279061 A279062 A279063

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Dec 05 2016

STATUS

approved

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Last modified October 1 15:05 EDT 2020. Contains 337443 sequences. (Running on oeis4.)