A392090 The unitary totient of the smallest cubefull number that is divisible by n.

1, 7, 26, 7, 124, 182, 342, 7, 26, 868, 1330, 182, 2196, 2394, 3224, 15, 4912, 182, 6858, 868, 8892, 9310, 12166, 182, 124, 15372, 26, 2394, 24388, 22568, 29790, 31, 34580, 34384, 42408, 182, 50652, 48006, 57096, 868, 68920, 62244, 79506, 9310, 3224, 85162, 103822

Offset

1,2

Comments

First differs from the sequence of absolute values of A063453 at n = 16.

Links

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

Formula

a(n) = A047994(A356193(n)).

Multiplicative with a(p^e) = p^max(e, 3) - 1.

Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 + 1/p^(s-3) - 1/p^(s-1) - 2/p^s - 1/p^(2*s-4) + 2/p^(2*s-1) + 1/p^(4*s-4) - 1/p^(4*s-3)).

Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = zeta(3) * zeta(4) * Product_{p prime} (1 - 1/p^2 - 1/p^3 - 2/p^4 + 3/p^5 + 2/p^7 - 2/p^8 + 1/p^12 - 2/p^13 + 1/p^14) = 0.58988140992095483236... .

Mathematica

f[p_, e_] := p^Max[e, 3] - 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^max(f[i, 2], 3)-1); }

Crossrefs

Cf. A002117, A013662, A036966, A047994, A063453, A356193, A390756.

Sequence in context: A157702 A373162 A063453 * A392088 A284054 A284786

Adjacent sequences: A392087 A392088 A392089 * A392091 A392092 A392093

Keyword

nonn,mult,easy

Author

Amiram Eldar, Dec 30 2025

Status

approved