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

Author

Ant King, Apr 17 2007

Keywords

• easy
• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Maple

# 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

Mathematica

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

Formula

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