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

1,1

Comments

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

Links

Table of n, a(n) for n=1..36.

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

Cf. A006038, A091191.

Sequence in context: A243104 A006038 A287646 * A188439 A275472 A275066

Adjacent sequences: A316113 A316114 A316115 * A316117 A316118 A316119

Keyword

nonn

Author

David A. Corneth, Aug 18 2018

Status

approved