A316116 Least odd primitive abundant number having its prime signature.

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

Offset: 1

Author

David A. Corneth, Aug 18 2018

Keywords

• nonn

Comments

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

Examples

			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
		

Crossrefs

Cf. A006038, A091191.

Programs

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 *)