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A005088 Number of primes = 1 mod 3 dividing n. 8
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,91

COMMENTS

The first instance of a(n)=2 is for n=91; the first instance of a(n)=3 is for n=1729.  1729 is famously Ramanujan's taxi cab number -- see A001235. - Harvey P. Dale, Jun 25 2013

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

S. R. Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math/0604465 [math.NT], 2006-2016.

FORMULA

Additive with a(p^e) = 1 if p = 1 (mod 3), 0 otherwise.

From Antti Karttunen, Jul 10 2017: (Start)

a(1) = 0; for n > 1, ((A020639(n) mod 3) mod 2) + a(A028234(n)).

a(n) = A001221(n) - A005090(n) - A079978(n).

(End)

MATHEMATICA

Join[{0}, Table[Count[Transpose[FactorInteger[n]][[1]], _?(Mod[#, 3]==1&)], {n, 2, 90}]] (* Harvey P. Dale, Jun 25 2013 *)

Array[DivisorSum[#, 1 &, And[PrimeQ@ #, Mod[#, 3] == 1] &] &, 91] (* Michael De Vlieger, Jul 11 2017 *)

PROG

(PARI) a(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i]%3==1) \\ Charles R Greathouse IV, Jan 16 2017

(Scheme) (define (A005088 n) (if (= 1 n) 0 (+ (modulo (modulo (A020639 n) 3) 2) (A005088 (A028234 n))))) ;; Antti Karttunen, Jul 10 2017

CROSSREFS

Cf. A001221, A005070, A005090, A020639, A028234, A079978.

Cf. A121940 (first number having n such factors).

Sequence in context: A131561 A110515 A071936 * A076142 A084904 A084928

Adjacent sequences:  A005085 A005086 A005087 * A005089 A005090 A005091

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)