Jean Luc Garambois has authored 4 sequences.
A365351
Exponents e such that the aliquot sequence starting with 2^e ends with a prime number at index 2.
Original entry on oeis.org
6, 11, 18, 27, 41, 74, 157, 197, 294, 549, 581
Offset: 1
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Select[Range[100], PrimeQ[DivisorSigma[1, 2^# - 1] - 2^# + 1] &] (* Amiram Eldar, Sep 02 2023 *)
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f(n) = sigma(n) - n; \\ A001065
isok(k) = ispseudoprime(f(f(2^k))); \\ Michel Marcus, Sep 02 2023
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def s(n):
sn = sigma(n) - n
return sn
e = 1
exponents_list = []
while e<=200:
m = 2^e
index = 0
if is_prime(s(s(m))):
exponents_list.append(e)
e+=1
print (exponents_list)
A358266
Numbers k such that the aliquot sequence of 2^k ends with the prime 7.
Original entry on oeis.org
3, 10, 12, 141, 278, 387, 421
Offset: 1
a(4)=141 because the aliquot sequence that starts with the integer 2^141 ends with the prime number 7 and there are only three smaller powers of 2 that do the same: 2^3, 2^10 and 2^12.
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f(n) = if (n==1, return(2)); my(list = List(), s=2^n); for (i=1, oo, s = sigma(s) - s; if (#select(x->(x==s), list), return(0)); if (isprime(s), return (s)); listput(list, s); );
isok(m) = f(m) == 7;
A358239
Numbers k such that the aliquot sequence of 2^k ends with the prime 3.
Original entry on oeis.org
2, 4, 55, 164, 305, 317
Offset: 1
a(3)=55 because the aliquot sequence that starts with the integer 2^55 ends with the prime number 3 and there are only two smaller powers of 2 that do the same: 2^2 and 2^4.
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f(n) = if (n==1, return(2)); my(list = List(), s=2^n); for (i=1, oo, s = sigma(s) - s; if (#select(x->(x==s), list), return(0)); if (isprime(s), return (s)); listput(list, s););
isok(m) = f(m) == 3; \\ Michel Marcus, Nov 05 2022
A238382
Untouchable amicable numbers: amicable pairs which cannot be reached by any aliquot sequence starting from a number that does not belong to this pair.
Original entry on oeis.org
356408, 399592, 643336, 652664, 5232010, 5799542, 9363584, 9437056, 10596368, 11199112, 15363832, 16517768, 31818952, 32205616, 34352624, 34860248, 46237730, 48641584, 48852176, 49215166, 52695376, 55349570, 56208368, 61319902, 91996816, 93259184
Offset: 1
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