A372924 a(n) = (sum_digits(n^3)-n)/3.
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, -1, -7, -1, -2, -2, -5, -3, -3, -6, -4, -4, -10, -5, -5, -5, -6, -9, -6, -10, -10, -7, -14, -11, -11, -6, -9, -9, -10, -10, -13, -11, -17, -11, -12, -15, -15, -13, -10
Offset: 0
Examples
For n=42, 42^3 = 74088 has sum of digits 27 so a(42) = (27 - 42)/3 = -5.
Crossrefs
Cf. A004164.
Programs
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C
#include
#include int32_t sumDigits(int64_t num) { int32_t sum = 0; while (num > 0) { sum += num % 10; num /= 10; } return sum; } int main() { for (int64_t i=0; i<10000; ++i) { int64_t num = i * i * i; int32_t sum = sumDigits(num); printf("%ld, ", (sum - i)/3); } return 0; } -
Maple
read("transforms"): A372924 := proc(n) (digsum(n^3)-n)/3 ; end proc: seq(A372924(n),n=0..80) ; # R. J. Mathar, Jul 03 2024 -
Mathematica
Table[(DigitSum[n^3] - n)/3, {n, 0, 100}] (* Paolo Xausa, Jul 03 2024 *)
Formula
a(n) = (A004164(n)-n)/3.
Comments