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A329730
Numbers k such that usigma(uphi(k)) = uphi(usigma(k)), where usigma is the sum of unitary divisors function (A034448) and uphi is the unitary totient function (A047994).
1
1, 3, 4, 8, 12, 24, 33, 91, 132, 201, 728, 812, 921, 1608, 1612, 2064, 2496, 2854, 3058, 3240, 3435, 3500, 4426, 5074, 5664, 5762, 6860, 7318, 7368, 8434, 9500, 9846, 10286, 11073, 12982, 13773, 14252, 14386, 17241, 17246, 18321, 18723, 18898, 19628, 21309, 21538
OFFSET
1,2
COMMENTS
The unitary version of A033632.
LINKS
EXAMPLE
33 is the sequence since usigma(uphi(33)) = usigma(20) = 30 and uphi(usigma(33)) = uphi(48) = 30.
MATHEMATICA
usigma[1]=1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); aQ[n_] := usigma[uphi[n]] == uphi[usigma[n]]; Select[Range[22000], aQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 19 2019
STATUS
approved