A030163 Solutions x of 2*uphi(x)=x, where uphi is the unitary phi function (A047994).

2, 12, 168, 240, 14880, 65280, 4294901760, 7608944640, 1125874137169920, 18446744069414584320

Offset: 1

Author

Yasutoshi Kohmoto

Keywords

• nonn
• more

Links

• Tomohiro Yamada, An analog of perfect numbers involving the unitary totient function, arXiv:1806.00647 [math.NT], 2018.

Crossrefs

Cf. A047994.

Programs

PARI

uphi(n) = my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1);
isok(n) = uphi(n) == n/2; \\ Michel Marcus, Feb 13 2018

PARI

solve_uphi(N, D, limit) = {my(g,f,uphi,sol,p,n,pn,uphipn,tmp,ll); sol = [];g = gcd(N, D); N /= g; D /= g; if (D==1, if (N==1, sol = [1]);sol;, f = factor(D); uphi = prod(i=1, #f~, f[i, 1]^f[i, 2]-1); if (uphi(x <= limit), vecsort(sol,,8));}
solve_uphi(1, 2, 10^20) \\ Michel Marcus, Jun 07 2018

Extensions

Corrected offset and keyword more by Michel Marcus, Feb 13 2018