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a(n) is the prime or perfect or amicable or sociable number encountered in the aliquot sequence for 2^n.
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%I #11 Nov 15 2022 10:47:14

%S 2,3,7,3,31,41,127,41,43,7,113,7,8191,6,6,313,131071,211457,524287,53,

%T 4217,433,41,547,2243,691921,21275809,673,76831,467,2147483647,89,

%U 112337,401,17681,9342799,12011,9511,19,1061129,164524721,5460123943,71,106661,33188053169,211,41

%N a(n) is the prime or perfect or amicable or sociable number encountered in the aliquot sequence for 2^n.

%H Michel Marcus, <a href="/A358415/b358415.txt">Table of n, a(n) for n = 1..200</a>

%H Jean-Luc Garambois, <a href="http://www.aliquotes.com/aliquotes_puissances_entieres/all/2.html">Aliquot sequences starting on integer powers 2^i</a>

%F a(n) = A115350(2^n).

%o (PARI) a(n) = my(b=2); if (n==1, return(b)); my(list = List(), s=b^n); for (i=1, oo, s = sigma(s) - s; if (#select(x->(x==s), list), return(s)); if (isprime(s), return (s)); listput(list, s););

%Y Cf. A001065, A115350, A358239, A358266.

%K nonn

%O 1,1

%A _Michel Marcus_, Nov 14 2022