OFFSET
1,2
COMMENTS
If k = Product_{i=1..t} p_i^e_i and phi(k) = S(k^n), then (p-1)*p^(e-1)*phi(k/p) = S(p^e), where p^e = Max_{i=1..t} S(p_i^e_i) and S(n) = A002034(n).
LINKS
Jinyuan Wang, Rows n = 1..359 of triangle, flattened
Bin Chen, An Equation Involving the Smarandache Function, Applied Mechanics and Materials (Volumes 204-208), 4785-4788, 2012.
EXAMPLE
Triangle begins:
1 | 1, 8, 9, 12, 18;
2 | 1, 24, 25, 50;
3 | 1, 32, 48, 49, 98;
4 | 1;
5 | 1, 64, 72, 121, 242;
6 | 1, 81, 96, 162, 169, 338;
...
PROG
(PARI) s(n) = {my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); k; }
f(n) = floor(n*exp(Euler)*log(log(n^2))+2.5*n/log(log(n^2)));
row(n) = {my(k, t, v=List([1])); while(4*n*(t++)>=2^t, forprime(p=2, if(t<3, t*n+1, sqrtnint(t*n, t-2)), for(m=1, f(1+s(p^(t*n))/(p-1)/p^(t-1)), if(eulerphi(k=m*p^t)==s(k^n), listput(v, k))))); Set(v); }
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Jinyuan Wang, Aug 05 2020
STATUS
approved