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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 MÃ¶bius 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.)