A319481 - OEIS

%I #9 Feb 11 2026 10:14:02

%S 1,2,6,12,168,240,14880,65280,4294901760,7608944640,1125874137169920,

%T 18446744069414584320

%N Integers k such that uphi(k) divides k, where uphi is the unitary phi function (A047994).

%C If it exists, a(13) > 10^150. - _Max Alekseyev_, Feb 10 2026

%H Tomohiro Yamada, <a href="https://arxiv.org/abs/1806.00647">An analog of perfect numbers involving the unitary totient function</a>, arXiv:1806.00647 [math.NT], 2018. See (2) on p. 2.

%o (PARI) uphi(n) = my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1);

%o isok(n) = frac(n/uphi(n)) == 0;

%Y Cf. A047994.

%Y A030163 is a subsequence.

%K nonn,more

%O 1,2

%A _Michel Marcus_, Sep 20 2018