A347115 Möbius transform of A341515.

1, 4, 1, 10, 2, 5, 4, 30, 2, 118, 6, 12, 10, 236, 2, 90, 12, 64, 16, 240, 4, 594, 18, 36, 6, 830, 4, 480, 22, -116, 28, 270, 6, 1428, 8, 132, 30, 1784, 10, 720, 36, 1076, 40, 1200, 4, 2622, 42, 108, 20, 144, 12, 1680, 46, 458, 12, 1440, 16, 4178, 52, -228, 58, 4772, 8, 810, 20, 1242, 60, 2880, 18, 2752, 66, 396

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to 3x+1 (or Collatz) problem

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A008683(n/d) * A341515(d).

Prog

(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A329603(n) = A005940(2+(3*A156552(n)));
A341515(n) = if(n%2, A064989(n), A329603(n));
A347115(n) = sumdiv(n, d, moebius(n/d)*A341515(d));

Crossrefs

Cf. A008683, A064989, A329603, A341515.

Cf. A285702 (odd bisection), A347116 (even bisection).

Cf. also A332463, A347117, A347118, A348045.

Sequence in context: A209385 A121529 A304429 * A006370 A262370 A108759

Adjacent sequences: A347112 A347113 A347114 * A347116 A347117 A347118

Keyword

sign

Author

Antti Karttunen, Aug 20 2021

Status

approved