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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.
1
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
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
KEYWORD
nonn
AUTHOR
Mark Mansley, Nov 19 2013
STATUS
approved