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

1,1

Links

Table of n, a(n) for n=1..10.

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

Prog

(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<N, sol=[], sol = []; p = f[length(f~), 1]; n = f[length(f~), 2]; pn = p^n; uphipn = p^n-1; while(pn<=limit, tmp = solve_uphi(N*pn, D*uphipn, limit/pn); for (i=1, length(tmp), if (gcd(pn, tmp[i])==1, sol = concat(sol, pn*tmp[i]); ); ); n++; pn *= p; uphipn = p^n-1; ); if (uphi == N, sol = concat(sol, [D])); ); ); select(x->(x <= limit), vecsort(sol, , 8)); }
solve_uphi(1, 2, 10^20) \\ Michel Marcus, Jun 07 2018

Crossrefs

Cf. A047994.

Sequence in context: A201007 A226058 A120958 * A368981 A255163 A052728

Adjacent sequences: A030160 A030161 A030162 * A030164 A030165 A030166

Keyword

nonn,more

Author

Yasutoshi Kohmoto

Extensions

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

Status

approved