cp's OEIS Frontend

A372924 a(n) = (sum_digits(n^3)-n)/3.

%I A372924 #28 Jul 03 2024 09:27:26
%S A372924 0,0,2,2,2,1,1,1,0,3,-3,-1,2,2,1,1,1,0,0,3,-4,-1,-1,-2,-2,-2,0,0,-3,
%T A372924 -1,-7,-1,-2,-2,-5,-3,-3,-6,-4,-4,-10,-5,-5,-5,-6,-9,-6,-10,-10,-7,
%U A372924 -14,-11,-11,-6,-9,-9,-10,-10,-13,-11,-17,-11,-12,-15,-15,-13,-10
%N A372924 a(n) = (sum_digits(n^3)-n)/3.
%C A372924 a(n) + floor((n+1)/3) is always a multiple of 3. - _Jon E. Schoenfield_, May 18 2024
%F A372924 a(n) = (A004164(n)-n)/3.
%e A372924 For n=42, 42^3 = 74088 has sum of digits 27 so a(42) = (27 - 42)/3 = -5.
%p A372924 read("transforms"):
%p A372924 A372924 := proc(n)
%p A372924     (digsum(n^3)-n)/3 ;
%p A372924 end proc:
%p A372924 seq(A372924(n),n=0..80) ; # _R. J. Mathar_, Jul 03 2024
%t A372924 Table[(DigitSum[n^3] - n)/3, {n, 0, 100}] (* _Paolo Xausa_, Jul 03 2024 *)
%o A372924 (C)
%o A372924 #include <stdint.h>
%o A372924 #include <stdio.h>
%o A372924 int32_t sumDigits(int64_t num)
%o A372924 {
%o A372924   int32_t sum = 0;
%o A372924   while (num > 0)
%o A372924   {
%o A372924     sum += num % 10;
%o A372924     num /= 10;
%o A372924   }
%o A372924   return sum;
%o A372924 }
%o A372924 int main()
%o A372924 {
%o A372924   for (int64_t i=0; i<10000; ++i)
%o A372924   {
%o A372924     int64_t num = i * i * i;
%o A372924     int32_t sum = sumDigits(num);
%o A372924     printf("%ld, ", (sum - i)/3);
%o A372924   }
%o A372924   return 0;
%o A372924 }
%Y A372924 Cf. A004164.
%K A372924 sign,base,easy
%O A372924 0,3
%A A372924 _Guy Harari_, May 16 2024