A129486 -id:A129486 - cp's OEIS frontend

A129485 Odd unitary abundant numbers.

15015, 19635, 21945, 23205, 25935, 26565, 31395, 33495, 33915, 35805, 39585, 41055, 42315, 42735, 45885, 47355, 49665, 50505, 51765, 54285, 55965, 58695, 61215, 64155, 68145, 70455, 72345, 77385, 80535, 82005, 83265, 84315, 91245, 95865, 102795, 112035

Offset: 1

Ant King, Apr 17 2007

This sequence is different from A112643. The two sequences agree for the first 50 terms but differ thereafter. The exceptions, i.e. those odd unitary abundant numbers that are not squarefree ordinary abundant numbers, are in A129486.
22309287 is the smallest term not divisible by 5. 33426748355 is the smallest term not divisible by 3. - Donovan Johnson, May 15 2013
The numbers of terms not exceeding 10^k, for k = 5, 6, ..., are 34, 137, 1714, 16918, 181744, 1752337, 17290556, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00017... . - Amiram Eldar, Sep 02 2022

			The third odd unitary abundant number is 21945. Hence a(3) = 21945.

Donovan Johnson, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Unitary Divisor.

Cf. A034683, A129486, A034460, A034448, A129487, A002827, A129468, A112643.

# see A034683 for the code of isA034683()
isA129485 := proc(n)
    type(n,'odd') and isA034683(n) ;
end proc:
for n from 1 do
    if isA129485(n) then
        print(n);
    end if;
end do: # R. J. Mathar, Nov 10 2014

UnitaryDivisors[n_Integer?Positive]:=Select[Divisors[n],GCD[ #,n/# ]==1&];sstar[n_]:=Plus@@UnitaryDivisors[n]-n;Select[Range[1,10^5,2],sstar[ # ]># &]

This sequence contains the odd members of A034683. i.e. odd numbers with a positive unitary abundance (A129468).

A292705 Nonsquarefree unitary abundant numbers.

Original entry on oeis.org

150, 294, 420, 630, 660, 726, 750, 780, 840, 924, 990, 1014, 1020, 1050, 1092, 1140, 1170, 1380, 1386, 1428, 1470, 1530, 1596, 1638, 1650, 1710, 1734, 1740, 1860, 1890, 1950, 2058, 2070, 2142, 2166, 2220, 2394, 2460, 2550, 2580, 2610, 2790, 2820, 2850, 2940

Offset: 1

Amiram Eldar, Sep 21 2017

nonn

Most unitary abundant numbers are squarefree. For example, there are 70030 unitary abundant numbers below 10^6, and only 14685 are nonsquarefree.

The odd terms of this sequence are A129486.

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

Cf. A013929, A034683, A129486.

usigma[n_]:=If[n==1, 1, Times @@ (1 + Power @@@ FactorInteger[n])];
aQ[n_]:=!SquareFreeQ[n] && usigma[n] > 2 n; Select[Range[10^4], aQ]

cp's OEIS Frontend

A129485 Odd unitary abundant numbers.

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