A394481 a(n) = usigma(n) + tau(n) - tau(rad(n)).

1, 3, 4, 6, 6, 12, 8, 11, 11, 18, 12, 22, 14, 24, 24, 20, 18, 32, 20, 32, 32, 36, 24, 40, 27, 42, 30, 42, 30, 72, 32, 37, 48, 54, 48, 55, 38, 60, 56, 58, 42, 96, 44, 62, 62, 72, 48, 74, 51, 80, 72, 72, 54, 88, 72, 76, 80, 90, 60, 124, 62, 96, 82, 70, 84, 144, 68, 92, 96, 144, 72, 98, 74, 114, 106, 102, 96, 168, 80, 108, 85, 126, 84, 164, 108

Offset

1,2

Comments

For each divisor d of n, add d if d is a unitary divisor of n, else add 1.

Links

Table of n, a(n) for n=1..85.

Formula

a(n) = Sum_{d|n} d^[GCD(d,n/d) = 1], where [ ] is the Iverson bracket.

a(n) = A034448(n) + A000005(n) - A034444(n).

a(p^k) = p^k+k for p prime and k>=0. - Wesley Ivan Hurt, May 23 2026

Example

a(24) = 1^1 + 2^0 + 3^1 + 4^0 + 6^0 + 8^1 + 12^0 + 24^1 = 40.

Mathematica

Table[Sum[d^KroneckerDelta[GCD[d, n/d], 1], {d, Divisors[n]}], {n, 100}]

Crossrefs

Cf. A000005 (tau), A007947 (rad), A034444, A034448 (usigma), A387633.

Sequence in context: A275258 A230593 A304411 * A360522 A379497 A332619

Adjacent sequences: A394478 A394479 A394480 * A394482 A394483 A394484

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Mar 21 2026

Status

approved