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%I #15 Oct 29 2023 11:28:04
%S 945,6,20,88,272,1184,4288,16768,65792,266752,1055744,4204544,
%T 16789504,67248128,268877824,1073840128,4295032832,17183670272,
%U 68720263168,274888916992,1099518967808,4398082162688,17592248958976
%N Smallest primitive abundant number or perfect number with 2^n as a factor.
%C For n>=1, a(n) = 2^n*A014210(n). - _Michel Marcus_, Mar 07 2013
%e 945=3^3*5*7 least primitive abundant number with no factor 2, a(0)=945
%e 6=2*3 perfect number, a(1)=6
%e 20=2^2*5 primitive abundant number < 28=2^2*7 perfect number, a(2)=20
%e 88=2^3*11
%e 272=2^4*17
%e 1184=2^5*37
%e 4288=2^6*67
%e 16768=2^7*131
%e 65792=2^8*257
%e 266752=2^9*521
%t {945}~Join~Array[2^#*Prime[1 + PrimePi[2^#]] &, 22] (* _Michael De Vlieger_, Oct 29 2023 *)
%o (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);}
%o a(n) = {p = 2^n; k = 3; while (1, v = p * k; if (isprab(v), return (v)); k += 2;); \\ _Michel Marcus_, Mar 07 2013
%Y Cf. A000079, A000203, A014210.
%K nonn
%O 0,1
%A _Pierre CAMI_, Jan 06 2008
%E More terms from _Michel Marcus_, Mar 07 2013
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