A366376 -id:A366376 - cp's OEIS frontend

A332214 Mersenne-prime fixing variant of permutation A163511: a(n) = A332212(A163511(n)).

1, 2, 4, 3, 8, 9, 6, 7, 16, 27, 18, 49, 12, 21, 14, 5, 32, 81, 54, 343, 36, 147, 98, 25, 24, 63, 42, 35, 28, 15, 10, 31, 64, 243, 162, 2401, 108, 1029, 686, 125, 72, 441, 294, 175, 196, 75, 50, 961, 48, 189, 126, 245, 84, 105, 70, 155, 56, 45, 30, 217, 20, 93, 62, 11, 128, 729, 486, 16807, 324, 7203, 4802, 625, 216, 3087, 2058, 875

Offset: 0

Antti Karttunen, Feb 09 2020

Any Mersenne prime (A000668) times any power of 2, i.e., sequence A335431, is fixed by this map (note the indexing), including also all even perfect numbers. It is not currently known whether there are any additional fixed points.

Because a(n) has the same prime signature as A163511(n), it implies that applying A046523 and A052409 to this sequence gives the same results as with A163511, namely, sequences A278531 and A365805. - Antti Karttunen, Oct 09 2023

Cf. A163511, A332211, A332212, A332215 (inverse permutation).
Cf. A278531 [= A046523(a(n))], A290251 [= A001222(a(n))], A365805 [= A052409(a(n))], A366372 [= a(n)-n], A366373 [= gcd(n,a(n))], A366374 (numerator of n/a(n)), A366375 (denominator of n/a(n)), A366376.
Cf. A000043, A000668, A000396, A324200, A335431 (conjectured to give all the fixed points).

PARI
```
A332214(n) = A332212(A163511(n));
```

\\ Needs precomputed data for A332211:
v332211 = readvec("b332211_to.txt"); \\ Prepared with gawk ' { print $2 } ' < b332211.txt > b332211_to.txt
A332211(n) = v332211[n];
A332214(n) = if(!n, 1, my(i=1, p=A332211(i), t=1); while(n>1, if(!(n%2), (t*=p), i++; p=A332211(i)); n >>= 1); (t*p)); \\ Antti Karttunen, Oct 09 2023

a(n) = A332212(A163511(n)).

A366373 a(n) = gcd(n, A332214(n)), where A332214 is the Mersenne-prime fixing variant of permutation A163511.

Original entry on oeis.org

1, 1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 1, 12, 1, 14, 5, 16, 1, 18, 1, 4, 21, 2, 1, 24, 1, 2, 1, 28, 1, 10, 31, 32, 3, 2, 7, 36, 1, 2, 1, 8, 1, 42, 1, 4, 15, 2, 1, 48, 7, 2, 1, 4, 1, 2, 5, 56, 3, 2, 1, 20, 1, 62, 1, 64, 1, 6, 1, 4, 3, 14, 1, 72, 1, 2, 25, 4, 1, 2, 1, 16, 27, 2, 1, 84, 5, 2, 1, 8, 1, 30, 7, 4, 93, 2, 1, 96

Offset: 0

Antti Karttunen, Oct 08 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A332214, A366372, A366374, A366375, A366376.

Cf. also A364254, A364255, A366283.

PARI
```
A366373(n) = gcd(n,A332214(n));
```

a(n) = gcd(n, A366372(n)) = gcd(A332214(n), A366372(n)).
For n >= 1, a(n) = n / A366374(n)
a(n) = A332214(n) / A366375(n).

A366375 a(n) = A332214(n) / gcd(n, A332214(n)), where A332214 is the Mersenne-prime fixing variant of permutation A163511.

Original entry on oeis.org

1, 2, 2, 1, 2, 9, 1, 1, 2, 3, 9, 49, 1, 21, 1, 1, 2, 81, 3, 343, 9, 7, 49, 25, 1, 63, 21, 35, 1, 15, 1, 1, 2, 81, 81, 343, 3, 1029, 343, 125, 9, 441, 7, 175, 49, 5, 25, 961, 1, 27, 63, 245, 21, 105, 35, 31, 1, 15, 15, 217, 1, 93, 1, 11, 2, 729, 81, 16807, 81, 2401, 343, 625, 3, 3087, 1029, 35, 343, 375, 125, 29791, 9, 49

Offset: 0

Antti Karttunen, Oct 08 2023

Denominator of n / A332214(n).

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A332214, A366372, A366373, A366374 (numerators), A366376 (rgs-transform).

Cf. also A364492, A366285.

A366375(n) = (A332214(n)/gcd(n,A332214(n)));

a(n) = A332214(n) / A366373(n) = A332214(n) / gcd(n, A332214(n)).

A366372 a(n) = A332214(n) - n, where A332214 is the Mersenne-prime fixing variant of permutation A163511.

Original entry on oeis.org

1, 1, 2, 0, 4, 4, 0, 0, 8, 18, 8, 38, 0, 8, 0, -10, 16, 64, 36, 324, 16, 126, 76, 2, 0, 38, 16, 8, 0, -14, -20, 0, 32, 210, 128, 2366, 72, 992, 648, 86, 32, 400, 252, 132, 152, 30, 4, 914, 0, 140, 76, 194, 32, 52, 16, 100, 0, -12, -28, 158, -40, 32, 0, -52, 64, 664, 420, 16740, 256, 7134, 4732, 554, 144, 3014, 1984

Offset: 0

Antti Karttunen, Oct 08 2023

sign

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A332214, A335431 (known positions of 0's), A366373, A366374, A366375, A366376.

Cf. also A364253, A364258, A366282.

PARI
```
A366372(n) = (A332214(n)-n);
```

A366374 a(n) = n / gcd(n, A332214(n)), where A332214 is the Mersenne-prime fixing variant of permutation A163511.

Original entry on oeis.org

0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 11, 1, 13, 1, 3, 1, 17, 1, 19, 5, 1, 11, 23, 1, 25, 13, 27, 1, 29, 3, 1, 1, 11, 17, 5, 1, 37, 19, 39, 5, 41, 1, 43, 11, 3, 23, 47, 1, 7, 25, 51, 13, 53, 27, 11, 1, 19, 29, 59, 3, 61, 1, 63, 1, 65, 11, 67, 17, 23, 5, 71, 1, 73, 37, 3, 19, 77, 39, 79, 5, 3, 41, 83, 1, 17, 43, 87, 11, 89

Offset: 0

Antti Karttunen, Oct 08 2023

Numerator of n / A332214(n).

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A332214, A366372, A366373, A366375 (denominators), A366376.

Cf. also A364491, A366284.

PARI
```
A366374(n) = (n/gcd(n,A332214(n)));
```

a(n) = n / A366373(n) = n / gcd(n, A332214(n)).

cp's OEIS Frontend

A332214 Mersenne-prime fixing variant of permutation A163511: a(n) = A332212(A163511(n)).

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Formula

A366373 a(n) = gcd(n, A332214(n)), where A332214 is the Mersenne-prime fixing variant of permutation A163511.

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PARI

Formula

A366375 a(n) = A332214(n) / gcd(n, A332214(n)), where A332214 is the Mersenne-prime fixing variant of permutation A163511.

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Author

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Programs

PARI

Formula

A366372 a(n) = A332214(n) - n, where A332214 is the Mersenne-prime fixing variant of permutation A163511.

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Author

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Links

Crossrefs

Programs

PARI

A366374 a(n) = n / gcd(n, A332214(n)), where A332214 is the Mersenne-prime fixing variant of permutation A163511.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula