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A133814 Smallest primitive abundant number or perfect number with 2^n as a factor. 0
945, 6, 20, 88, 272, 1184, 4288, 16768, 65792, 266752, 1055744, 4204544, 16789504, 67248128, 268877824, 1073840128, 4295032832, 17183670272, 68720263168, 274888916992, 1099518967808, 4398082162688, 17592248958976 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..22.

EXAMPLE

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

PROG

(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

CROSSREFS

Sequence in context: A145493 A271765 A343330 * A104438 A125013 A294576

Adjacent sequences:  A133811 A133812 A133813 * A133815 A133816 A133817

KEYWORD

nonn

AUTHOR

Pierre CAMI, Jan 06 2008

EXTENSIONS

More terms from Michel Marcus, Mar 07 2013

STATUS

approved

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Last modified December 6 04:20 EST 2021. Contains 349562 sequences. (Running on oeis4.)