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

1,1

Links

Table of n, a(n) for n=1..41.

Example

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).

Prog

(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

Crossrefs

Supersequence of A083873.

Cf. A025487, A071395.

Sequence in context: A234367 A071395 A362053 * A335557 A245856 A053741

Adjacent sequences: A357918 A357919 A357920 * A357922 A357923 A357924

Keyword

nonn

Author

David A. Corneth, Oct 20 2022

Status

approved