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 A005088 Number of primes = 1 mod 3 dividing n. 9
 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) MAPLE A005088 := proc(n)     local a, pe;     a := 0 ;     for pe in ifactors(n)[2] do         if modp(op(1, pe), 3)= 1 then             a := a+1 ;         end if;     end do:     a ; end proc: # R. J. Mathar, May 19 2020 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 STATUS approved

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Last modified May 12 21:06 EDT 2021. Contains 343829 sequences. (Running on oeis4.)