A364566 -id:A364566 - cp's OEIS frontend

A364558 a(n) = A364557(n) - A000010(n), where A364557 is the Möbius transform of A005941, and A000010 (Euler phi) is the Möbius transform of A000027.

0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 6, 0, 20, 2, -4, 0, 48, -2, 110, 0, -4, 6, 234, 0, -12, 20, -10, 4, 484, -4, 994, 0, -4, 48, -16, -4, 2012, 110, 8, 0, 4056, -4, 8150, 12, -16, 234, 16338, 0, -26, -12, 32, 40, 32716, -10, -24, 8, 92, 484, 65478, -8, 131012, 994, -20, 0, -16, -4, 262078, 96, 212, -16, 524218, -8, 1048504

Offset: 1

Antti Karttunen, Jul 28 2023

sign

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

Cf. A000010, A005941, A364557, A364559 (inverse Möbius transform), A364565 (positions of 0's), A364566 (of terms < 0).

PARI
```
A364558(n) = (A364557(n)-eulerphi(n));
```

from math import prod
from sympy import factorint, primepi
def A364558(n): return (1<1 else 0 # Chai Wah Wu, Jul 29 2023

A364565 Numbers k at which point A364557 (the Möbius transform of A005941) is equal to A000010 (Euler phi function).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 40, 48, 64, 80, 85, 96, 128, 160, 170, 192, 256, 320, 340, 384, 512, 640, 680, 768, 1024, 1280, 1360, 1536, 2048, 2560, 2720, 3072, 4096, 5120, 5440, 6144, 8192, 10240, 10880, 12288, 16384, 20480, 21760, 24576, 32768, 40960, 43520, 49152, 65536, 81920, 87040, 98304, 131072

Offset: 1

Antti Karttunen, Jul 29 2023

nonn

Question: Are there any other odd terms apart from 1, 3, 5, 85?

Positions of 0's in A364558.

Cf. A000010, A029747, A364557, A364566.

A364557(n) = if(1==n, 1, 2^(primepi(vecmax(factor(n)[, 1]))+(bigomega(n)-omega(n))-1));
isA364565(n) = (A364557(n)==eulerphi(n));

cp's OEIS Frontend

A364558 a(n) = A364557(n) - A000010(n), where A364557 is the Möbius transform of A005941, and A000010 (Euler phi) is the Möbius transform of A000027.

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