Comments by Erik Huang: A006753 Smith numbers: composite numbers n such that sum of digits of n = sum of digits of prime factors of n (counted with multiplicity). GP code: isA006753(n) = if(isprime(n), 0, my(f=factor(n)); sum(i=1, #f[, 1], sumdigits(f[i,1])*f[i, 2]) == sumdigits(n)) for(i=1, 1e6, isA006753(i) && print (i)) Comments: On the spectrogram, there's one significant spectral peak at 4894 Hz and 3 more peaks that are multiples of this frequency. Dividing such frequency into our sample frequency and we get number 9.0 To find a relationship between number 9 and smith number sequence, here is the counts in residue classes mod 9 up to 10^6: [4368, 763, 1220, 2633, 10711, 903, 6497, 499, 2334] Among these counts, (4 mod 9) is the most dominant one. To explain this effect, we investigated in properties of prime factors and found: For every smith number that has 2 prime factors, it is always congruent to 4 mod 9 For every smith number that has 3 prime factors, it is can be congruent to 3 mod 9 or 6 mod 9 .... Note that lots of small integers are made of 2 prime factors; Having more prime factors also results in an increase in sum of digits. This phenomena lasts even when numbers get large We counted the residue classes mod 9 in the interval from 10^10 to 10^10+10^6: [414, 128, 238, 381, 3413, 159, 759, 85, 400]