# [seqfan] Re: UnitaryPhi

zbi74583_boat at yahoo.co.jp zbi74583_boat at yahoo.co.jp
Tue Sep 4 06:38:31 CEST 2018

```    Hi Michel  Bob
Thanks for computing these terms

I computed a(20)
2^12*3^6*5^2*7^3*13^2

It is confirmed comparing your result
Some other n : UnitaryPhi(n)=19/20*n
2^12*3^9*5^3*7^3*13^2*31*757
2^12*3^9*5^2*7^3*13^3*757
2^12*3^7*5^3*7^3*13^2*31*1093
2^12*3^7*5^2*7^3*13^2*1093
2^12*3^6*5^3*7^3*13^2*31

I have computed a(24)

2^22*3^5*5^3*11^4*31^2*61*89*683

Could anyone confirm it?

To Ami
I computed it mentally ^o^  It is impossible to do the exhaustive search up to 10^24

Yasutoshi

----- Original Message -----

> Cc:

> Date: 2018/9/2, Sun 13:55
> Subject: [seqfan] Re: UnitaryPhi
>
> or 0 if unknnown.
> {2, 3, 4, 5, 144, 7, 8, 9, 400, 11, 64281600, 13, 84672, 129600, 16, 17, 518400,
> 19, 0, 254016, 0, 23, 0, 25, 0, 27, 3136, 29, 0, 31, 32, 0, 0, 0, 5184, 37, 0,
> 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 49, 0, 5992704, 0, 53, 0, 0, 0, 0, 0, 59, 0,
> 61, 0, 0, 64, 0, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 81, 0, 83, 0,
> 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0}
> a(pp) = pp iff pp is a prime power (A000961) > 1.
>
> -----Original Message-----

> Sent: Friday, 31 August, 2018 10:41 AM

> Subject: [seqfan] Re: UnitaryPhi

>
> a(12)=64281600 (and I didn't do it mentally...)
>

>
>>      Hi Seqfans    See A145680  It is defined as follow
>>      The smallest number m such that UnitarySigma(m)=(n+1)/n*m
>>      I replaced UniitarySigma by   UnitaryPhi
>>      The smallest number m such that UnitaryPhi(m)=(n-1)/n*m
>>      a(n) : 2, 3, 4, 5, 144, 7, 8, 9, 400, 11, -, 13, 2^12*3^4*5^2*7^2,
>>  2^9*3^4*5^2*73, 16, 17, 2^8*3^4*5^2, 19, -
>>      I computed some term   mentally  Could anyone confirm them and compute
>>  more terms?  Still a(12) is unknown
>>
>>
>>      Yasutoshi
>>
>>  --
>>  Seqfan Mailing list - http://list.seqfan.eu/
>>
>
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```