A358266 -id:A358266 - cp's OEIS frontend

A358415 a(n) is the prime or perfect or amicable or sociable number encountered in the aliquot sequence for 2^n.

2, 3, 7, 3, 31, 41, 127, 41, 43, 7, 113, 7, 8191, 6, 6, 313, 131071, 211457, 524287, 53, 4217, 433, 41, 547, 2243, 691921, 21275809, 673, 76831, 467, 2147483647, 89, 112337, 401, 17681, 9342799, 12011, 9511, 19, 1061129, 164524721, 5460123943, 71, 106661, 33188053169, 211, 41

Offset: 1

Michel Marcus, Nov 14 2022

nonn

Michel Marcus, Table of n, a(n) for n = 1..200
Jean-Luc Garambois, Aliquot sequences starting on integer powers 2^i

Cf. A001065, A115350, A358239, A358266.

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););

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

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

Jean Luc Garambois, Nov 04 2022

			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.

Jean-Luc Garambois, Aliquot sequences starting on integer powers n^i, n^i project.
Mersenne forum, n^i project.

Cf. A127163, A358266.

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

Define s(i) = sigma(i) - i = A000203(i) - i. Then k is a term of this sequence if the aliquot sequence obtained by repeatedly applying the mapping i->s(i) taking as initial value 2^k terminates in the prime 3.

cp's OEIS Frontend

A358415 a(n) is the prime or perfect or amicable or sociable number encountered in the aliquot sequence for 2^n.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula