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A348173
a(n) is the sum of the distinct values obtained when the unitary totient function is applied to the unitary divisors of n.
3
1, 1, 3, 4, 5, 3, 7, 8, 9, 5, 11, 12, 13, 7, 15, 16, 17, 9, 19, 20, 21, 11, 23, 24, 25, 13, 27, 28, 29, 15, 31, 32, 33, 17, 35, 36, 37, 19, 39, 40, 41, 21, 43, 44, 45, 23, 47, 48, 49, 25, 51, 52, 53, 27, 55, 56, 57, 29, 59, 60, 61, 31, 63, 64, 65, 33, 67, 68, 69, 35, 71, 72, 73, 37, 75, 76, 77, 39, 79, 80, 81, 41, 83, 78
OFFSET
1,3
COMMENTS
First differs from A283971 at n = 84.
LINKS
FORMULA
a(n) <= n, with equality if and only if n is in A348004.
EXAMPLE
The unitary divisors of 18 are {1, 2, 9, 18} and their uphi values are {1, 1, 8, 8}. The set of distinct values is {1, 8} whose sum is 9. Therefore, a(18) = 9.
MATHEMATICA
f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := Plus@@ DeleteDuplicates[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]; Array[a, 100]
CROSSREFS
The unitary version of A348158.
Sequence in context: A354998 A094758 A283971 * A100394 A178783 A156671
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 04 2021
STATUS
approved