

A316116


Least odd primitive abundant number having its prime signature.


0



945, 1575, 2205, 3465, 5775, 7425, 8085, 12705, 15015, 28215, 47025, 49875, 69825, 78975, 81081, 103455, 131625, 153153, 182325, 189189, 297297, 342225, 351351, 363375, 387345, 392445, 474045, 532875, 570375, 692835, 742203, 793611, 1102725, 1380825, 1468935, 1612875
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OFFSET

1,1


COMMENTS

Ordering of exponents matters; 1575 and 2205 have unordered prime signatures (2, 2, 1) and (2, 1, 2) respectively.


LINKS



EXAMPLE

1575 = 3^2 * 5^2 * 7 has prime signature (2, 2, 1) and is an odd primitive abundant number (A006038). Since 1575 is the smallest such number, it is in the sequence.  Michael B. Porter, Nov 24 2018


MATHEMATICA

lsig={}; lpab = {}; seq={}; Do[ d=Divisors[n]; If[Total[d] > 2 n && Intersection[ lpab, d] == {}, AppendTo[lpab, n]; sig=FactorInteger[n][[;; , 2]]; If[!MemberQ[ lsig, sig], AppendTo[seq, n]; AppendTo[lsig, sig]]], {n, 3, 1700000, 2}]; seq (* Amiram Eldar, Dec 09 2018 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



