[seqfan] A striking coincidence: A006863 vs. A143407

[Joerg Arndt]

About
 https://oeis.org/A006863  Denominator of B_{2n}/(-4n), where B_m are the Bernoulli numbers.
 https://oeis.org/A143407  Largest number k such that the reduced totient function psi(k) = A002174(n).

Looong lines needed:
A006863: 1, 24, 240, 504, 480, 264, 65520, 24, 16320, 28728, 13200, 552, 131040, 24, 6960, 171864, 32640, 24, 138181680, 24, 1082400, 151704, 5520, 1128, 4455360, 264, 12720, ...
A143407: 2, 24, 240, 504, 480, 264, 65520,     16320, 28728, 13200, 552, 131040,     6960, 171864, 32640,     138181680,     1082400, 151704, 5520, 1128, 4455360,      12720, ...

In A143407 there is the formula A143407(n) = A006863(A002174(n)/2) for n>1.
Is there any theorem/reference for this?

Best regards,   jj