A347118 -id:A347118 - cp's OEIS frontend

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

Antti Karttunen, Aug 20 2021

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Cf. A008683, A064989, A329603, A341515.
Cf. A285702 (odd bisection), A347116 (even bisection).
Cf. also A332463, A347117, A347118, A348045.

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));

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

A347117 Möbius transform of A329603.

Original entry on oeis.org

2, 3, 6, 10, 16, 0, 48, 30, 12, 104, 96, 12, 240, 192, 8, 90, 336, 54, 576, 240, 16, 504, 720, 36, 24, 600, 40, 480, 1056, -122, 1680, 270, 96, 1104, 96, 132, 1920, 1224, 144, 720, 2736, 1064, 3360, 1200, 0, 1920, 3696, 108, 60, 126, 624, 1680, 4416, 422, 336, 1440, 768, 3144, 5616, -228, 6960, 3120, 416, 810, 624

Offset: 1

Antti Karttunen, Aug 21 2021

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Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from indices in prime factorization

Cf. A008683, A156552, A329603.

Cf. also A332463, A347115, A347118.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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)));
A347117(n) = sumdiv(n,d,moebius(n/d)*A329603(d));

a(n) = Sum_{d|n} A008683(n/d) * A329603(d).

cp's OEIS Frontend

A347115 Möbius transform of A341515.

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