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

945, 6, 20, 88, 272, 1184, 4288, 16768, 65792, 266752, 1055744, 4204544, 16789504, 67248128, 268877824, 1073840128, 4295032832, 17183670272, 68720263168, 274888916992, 1099518967808, 4398082162688, 17592248958976

Offset: 0

Author

Pierre CAMI, Jan 06 2008

Keywords

• nonn

Comments

For n>=1, a(n) = 2^n*A014210(n). - Michel Marcus, Mar 07 2013

Examples

			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
		

Crossrefs

Cf. A000079, A000203, A014210.

Programs

Mathematica

{945}~Join~Array[2^#*Prime[1 + PrimePi[2^#]] &, 22] (* Michael De Vlieger, Oct 29 2023 *)

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);}
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

Extensions

More terms from Michel Marcus, Mar 07 2013