A364253 -id:A364253 - cp's OEIS frontend

A364288 a(n) = n - A243071(n).

1, 1, 0, 2, -2, 0, -8, 4, 4, -4, -20, 0, -50, -16, 2, 8, -110, 8, -236, -8, -8, -40, -488, 0, 14, -100, 18, -32, -994, 4, -2016, 16, -28, -220, 8, 16, -4058, -472, -86, -16, -8150, -16, -16340, -80, 20, -976, -32720, 0, 26, 28, -202, -200, -65482, 36, -4, -64, -452, -1988, -131012, 8, -262082, -4032, 6, 32, -58, -56

Offset: 1

Antti Karttunen, Jul 25 2023

sign

Antti Karttunen, Table of n, a(n) for n = 1..12288

Cf. A243071, A364256 [= gcd(n,a(n))], A364258.
Cf. A007283 (positions of 0's, conjectured), A364289 (positions of terms <= 0), A364290 (of terms > 0), A364291 (of terms >= 0).
Cf. also A364253.

nn = 60; f[x_] := Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First[#], Last[#] ] &@ Transpose@ FactorInteger@ x; Do[a[n] = Which[n <= 2, n - 1, OddQ[n], 1 + 2 a[f[n]], True, 2 a[n/2] ], {n, nn}]; Array[# - a[#] &, nn] (* Michael De Vlieger, Jul 25 2023 *)

A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A243071(n) = if(n<=2, n-1, if(!(n%2), 2*A243071(n/2), 1+(2*A243071(A064989(n)))));
A364288(n) = (n-A243071(n));

a(n) = A364258(A243071(n)).
For n >= 1, a(2*n) = 2*a(n).
For n >= 0, a(A007283(n)) = 0.

A364254 a(n) = gcd(n, A332215(n)).

Original entry on oeis.org

1, 1, 3, 2, 5, 6, 7, 4, 1, 10, 1, 12, 1, 14, 1, 8, 1, 2, 1, 20, 1, 2, 23, 24, 1, 2, 9, 28, 1, 2, 31, 16, 1, 2, 1, 4, 1, 2, 1, 40, 1, 2, 1, 4, 3, 46, 1, 48, 1, 2, 1, 4, 1, 18, 1, 56, 1, 2, 1, 4, 1, 62, 1, 32, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 15, 4, 1, 2, 1, 80, 1, 2, 1, 4, 5, 2, 1, 8, 1, 6, 13, 92, 1, 2, 1, 96, 1, 2, 3, 4

Offset: 1

Antti Karttunen, Jul 16 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A332215, A364253.

Cf. also A364255.

a(n) = gcd(n, A364253(n)) = gcd(A332215(n), A364253(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);
```

cp's OEIS Frontend

A364288 a(n) = n - A243071(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A364254 a(n) = gcd(n, A332215(n)).

Views

Author

Keywords

Links

Crossrefs

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

PARI