cp's OEIS Frontend

A133814 Smallest primitive abundant number or perfect number with 2^n as a factor.

%I A133814 #18 Sep 24 2024 03:08:37
%S A133814 945,6,20,88,272,1184,4288,16768,65792,266752,1055744,4204544,
%T A133814 16789504,67248128,268877824,1073840128,4295032832,17183670272,
%U A133814 68720263168,274888916992,1099518967808,4398082162688,17592248958976
%N A133814 Smallest primitive abundant number or perfect number with 2^n as a factor.
%C A133814 For n>=1, a(n) = 2^n*A014210(n). - _Michel Marcus_, Mar 07 2013
%e A133814 945=3^3*5*7 least primitive abundant number with no factor 2, a(0)=945
%e A133814 6=2*3 perfect number, a(1)=6
%e A133814 20=2^2*5 primitive abundant number < 28=2^2*7 perfect number, a(2)=20
%e A133814 88=2^3*11
%e A133814 272=2^4*17
%e A133814 1184=2^5*37
%e A133814 4288=2^6*67
%e A133814 16768=2^7*131
%e A133814 65792=2^8*257
%e A133814 266752=2^9*521
%t A133814 {945}~Join~Array[2^#*Prime[1 + PrimePi[2^#]] &, 22] (* _Michael De Vlieger_, Oct 29 2023 *)
%o A133814 (PARI) isprab(v) = {my(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 A133814 a(n) = {my(p = 2^n, k = 3); while (1, v = p * k; if (isprab(v), return (v)); k += 2;);} \\ _Michel Marcus_, Mar 07 2013
%Y A133814 Cf. A000079, A000203, A014210.
%K A133814 nonn
%O A133814 0,1
%A A133814 _Pierre CAMI_, Jan 06 2008
%E A133814 More terms from _Michel Marcus_, Mar 07 2013