The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A030163

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A030163

Solutions x of 2*uphi(x)=x, where uphi is the unitary phi function (A047994).
(history; published version)

#19 by Bruno Berselli at Thu Sep 20 08:15:43 EDT 2018

STATUS

proposed

approved

#18 by Michel Marcus at Thu Sep 20 07:56:20 EDT 2018

STATUS

editing

proposed

#17 by Michel Marcus at Thu Sep 20 07:56:08 EDT 2018

PROG

(PARI) uphi(n) = prodmy(i=1, #nf=factor(n)~, n); prod(i=1, #f, f[1, i]^nf[2, i]-1);

STATUS

approved

editing

#16 by N. J. A. Sloane at Thu Jun 07 22:14:02 EDT 2018

STATUS

proposed

approved

#15 by Michel Marcus at Thu Jun 07 14:51:29 EDT 2018

STATUS

editing

proposed

#14 by Michel Marcus at Thu Jun 07 14:50:22 EDT 2018

PROG

(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

STATUS

approved

editing

Discussion

Thu Jun 07

14:51

Michel Marcus: program adapted from another code to find solutions to sigma(x)/x = q

#13 by N. J. A. Sloane at Tue Jun 05 10:05:43 EDT 2018

STATUS

proposed

approved

#12 by Michel Marcus at Tue Jun 05 09:46:53 EDT 2018

STATUS

editing

proposed

#11 by Michel Marcus at Tue Jun 05 09:41:17 EDT 2018

DATA

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

STATUS

proposed

editing

Discussion

Tue Jun 05

09:41

Michel Marcus: correction: the sequence was not increasing

#10 by Michel Marcus at Tue Jun 05 01:17:27 EDT 2018

STATUS

editing

proposed