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%I #20 Nov 21 2013 05:32:53
%S 4,8,10,16,32,44,50,64,110,128,130,135,136,152,154,170,184,225,232,
%T 250,256,315,405,484,495,512,525,592,656,675,676,688,735,752,848,850,
%U 884,944,950,988,1012,1024,1078,1125,1150,1155,1196,1210,1215,1250,1276,1292
%N 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.
%C Tentatively called advanced deficient numbers. Intended as a counterpart to primitive abundant numbers.
%C 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).
%C All powers of 2 >=4 are in the sequence.
%H Donovan Johnson, <a href="/A232168/b232168.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%o (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
%Y Cf. A005100, A005101, A071395.
%K nonn
%O 1,1
%A _Mark Mansley_, Nov 19 2013
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