A357921 Primitive abundant numbers for which there is no smaller primitive abundant number having the same ordered prime signature.

20, 70, 88, 272, 550, 572, 945, 1184, 1430, 1575, 2205, 3465, 4288, 5775, 7425, 8085, 12705, 15015, 16768, 24272, 28215, 47025, 49875, 65792, 69825, 78975, 81081, 103455, 131625, 152224, 153153, 182325, 189189, 266752, 297297, 342225, 351351, 363375, 387345, 392445, 474045

Offset: 1

Author

David A. Corneth, Oct 20 2022

Keywords

• nonn

Examples

			550 is in the sequence as it is primitive abundant and it is the smallest primitive abundant number having its prime signature (in this case (1,2,1)). No positive integer < 550 is a primitive abundant and has prime signature (1,2,1).
		

Crossrefs

Supersequence of A083873.

Cf. A025487, A071395.

Programs

PARI

upto(n) = { m = Map(); res = List(); forfactored(i = 1, n, if(!mapisdefined(m, i[2][,2]), if(isA071395(i[1]), mapput(m, i[2][,2], i[1]); listput(res, i[1]) ) ) ); res }
isA071395(v) = {if (sigma(v) <= 2*v, return (0)); fordiv (v, d, if ((d != v) && (sigma(d) >= 2*d), return (0)); ); return (1); } \\ isA071395 from Michel Marcus at A071395