A348173 - OEIS

A348173

a(n) is the sum of the distinct values obtained when the unitary totient function is applied to the unitary divisors of n.

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

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OFFSET

1,3

COMMENTS

First differs from A283971 at n = 84.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

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.

Cf. A047994, A077610, A283971, A348001, A348004.

Sequence in context: A354998 A094758 A283971 * A100394 A178783 A156671

Adjacent sequences: A348170 A348171 A348172 * A348174 A348175 A348176

KEYWORD

nonn

AUTHOR

Amiram Eldar, Oct 04 2021

STATUS

approved