A232168 Numbers n such that n is a deficient number and there exists a prime number p greater than the largest prime factor of n such that p*n is abundant.

4, 8, 10, 16, 32, 44, 50, 64, 110, 128, 130, 135, 136, 152, 154, 170, 184, 225, 232, 250, 256, 315, 405, 484, 495, 512, 525, 592, 656, 675, 676, 688, 735, 752, 848, 850, 884, 944, 950, 988, 1012, 1024, 1078, 1125, 1150, 1155, 1196, 1210, 1215, 1250, 1276, 1292

Offset

1,1

Comments

Tentatively called advanced deficient numbers. Intended as a counterpart to primitive abundant numbers.

All primitive abundant numbers can be linked to an advanced deficient number but not all advanced deficient numbers generate primitive abundant numbers (e.g. 250).

All powers of 2 >=4 are in the sequence.

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Example

10 is a deficient number but 7*10 is abundant and 7>5 the largest prime factor of 10. Similarly 44 is deficient but 44*13, 17 or 19 are abundant.

Prog

(PARI) for(n=2, 1292, if(sigma(n)<2*n, f=factorint(n); p=nextprime(f[omega(n), 1]+1); m=p*n; if(sigma(m)>2*m, print1(n ", ")))) \\ Donovan Johnson, Nov 19 2013

Crossrefs

Cf. A005100, A005101, A071395.

Sequence in context: A311005 A311006 A311007 * A046559 A032618 A311008

Adjacent sequences: A232165 A232166 A232167 * A232169 A232170 A232171

Keyword

nonn

Author

Mark Mansley, Nov 19 2013

Status

approved