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

1,1

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

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Unitary Divisor.

Formula

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

Example

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

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[ # ]># &]

Crossrefs

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

Sequence in context: A046391 A339938 A112643 * A360526 A249263 A335052

Adjacent sequences: A129482 A129483 A129484 * A129486 A129487 A129488

Keyword

easy,nonn

Author

Ant King, Apr 17 2007

Status

approved