Anand Numbers 1,80,108 - Complete Private Notes including Digital Root 9 and Ank-Garbh Invariances

This is the complete private research archive of the author on the classification of positive integers satisfying n = s(n)·τ(n), where s(n) is sum of decimal digits and τ(n) is number of divisors.Main Theorem (n ≥ 1): Only solutions are 1, 80, 108. Proof is based on τ(n) ≤ 2√n and s(n) ≤ 9k, giving bound n ≤ 5184, verified computationally up to 10^6. τ(0) is undefined, hence 0 is excluded.This restricted version contains ALL remarks reserved for future work and for the author's forthcoming book 'Manujatva' (Yoga Darshan):- Remark 9: Tetradic symmetry (0,1,8 only)- Remark 10-12: Digital Root 9 invariance in sum (1+80+108=189→9), product (8640→9), difference (108-80-1=27→9) and division (108/80=1.35→9)- Remark 13: Ank-Garbh - 108 contains digits 1,0,8 which generate 1 and 80- Remark 15: Triple binding - 108×80+1=8641 prime, (108-80)×1=28 perfect number- Remark 16: 108 is minimal 3-digit pandigital number formed from digits {0,1,8}- Appendix A,B: Why 0 and 8 are not separate solutions but embodied in 108This record is kept Restricted to preserve priority and timestamp (DOI) for future publications. The open version containing only main theorem will be published on arXiv (math.NT) and OEIS.Author: Kunwar Anand Singh, Independent Researcher, IndiaORCID linked.