%I #17 Nov 26 2025 15:59:41

%S 1,6,60,90,87360

%N Unitary multiply-perfect numbers: n divides usigma(n), where usigma is the sum of unitary divisors of n (A034448).

%C 10^13 < a(6) <= 146361946186458562560000. - _Giovanni Resta_, Aug 29 2019

%H Peter Hagis, Jr., <a href="https://www.fq.math.ca/Scanned/25-2/hagis.pdf">Lower bounds for unitary multiperfect numbers</a>, Fibonacci Quarterly, Vol. 22, No. 2 (1984), pp. 140-143.

%o (PARI)

%o A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448

%o isA327158(n) = (gcd(n,A034448(n))==n);

%Y Fixed points of A323166, positions of zeros in A327164.

%Y Cf. A002827 (a subsequence), A034448, A327163.

%Y Cf. also A007691.

%K nonn,more

%O 1,2

%A _Antti Karttunen_, Aug 28 2019