A369205 Numbers m such that A188999(A034448(m)) = k*m for some k, where A034448 and A188999 are respectively the unitary and the bi-unitary sigma function.
1, 2, 9, 10, 15, 18, 21, 30, 40, 42, 60, 120, 288, 567, 630, 720, 756, 1023, 1134, 1428, 2046, 2160, 2268, 2520, 3024, 3276, 3570, 4092, 6048, 8184, 8925, 9240, 11424, 11550, 15345, 17850, 18144, 30690, 35700, 46200, 57120, 85680, 147312, 285600, 491040, 556920
Offset: 1
Keywords
Examples
A034448(18) = 4 * 10 = 40 and A188999(40) = 15 * 6 = 90 = 5 * 18, so 18 is a term with k = 5.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..105
Crossrefs
Programs
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PARI
a034448(n) = {my(f,i,p,e);f=factor(n);for(i=1,#f~,p=f[i,1];e=f[i,2];f[i,1]=p^e+1;f[i,2]=1);factorback(f)}; a188999(n) = {my(f,i,p,e);f=factor(n);for(i=1,#f~,p=f[i,1];e=f[i,2];f[i,1]=if(e%2,(p^(e+1)-1)/(p-1),(p^(e+1)-1)/(p-1)-p^(e/2));f[i,2]=1);factorback(f)}; isok(n) = (a188999(a034448(n))%n) == 0;