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A133814
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Smallest primitive abundant number or perfect number with 2^n as a factor.
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0
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945, 6, 20, 88, 272, 1184, 4288, 16768, 65792, 266752, 1055744, 4204544, 16789504, 67248128, 268877824, 1073840128, 4295032832, 17183670272, 68720263168, 274888916992, 1099518967808, 4398082162688, 17592248958976
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OFFSET
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0,1
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COMMENTS
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LINKS
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EXAMPLE
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945=3^3*5*7 least primitive abundant number with no factor 2, a(0)=945
6=2*3 perfect number, a(1)=6
20=2^2*5 primitive abundant number < 28=2^2*7 perfect number, a(2)=20
88=2^3*11
272=2^4*17
1184=2^5*37
4288=2^6*67
16768=2^7*131
65792=2^8*257
266752=2^9*521
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MATHEMATICA
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PROG
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(PARI) isprab(v) = {sig = sigma(v); if (sig < 2*v, return (0)); if (sig == 2*v, return (1)); fordiv (v, d, if ((d != v) && (sigma(d)>=2*d), return (0)); ); return (1); }
a(n) = {p = 2^n; k = 3; while (1, v = p * k; if (isprab(v), return (v)); k += 2; ); \\ Michel Marcus, Mar 07 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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