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 A275969 Least k such that phi(k) has exactly n prime factors (counted with multiplicity). 2
 3, 5, 13, 17, 51, 85, 193, 257, 769, 1285, 3281, 4369, 12289, 21845, 49601, 65537, 196611, 327685, 786433, 1114129, 3158273, 5570645, 12648641, 16843009, 50397953, 84215045, 202113281, 286331153, 805384193, 1431655765, 3221225473, 8168859365, 12952273921 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Least k such that A001222(A000010(k)) = n. If 2^2^n + 1 is a Fermat prime (A019434), then a(2^n) = 2^2^n + 1. - Michael De Vlieger, Aug 15 2016 LINKS EXAMPLE a(2) = 5 because phi(5) = 4 has 2 prime factors (counted with multiplicity). MATHEMATICA Table[k = 1; While[PrimeOmega@ EulerPhi@ k != n, k++]; k, {n, 16}] (* Michael De Vlieger, Aug 15 2016 *) PROG (PARI) a(n) = {my(k = 1); while(bigomega(eulerphi(k)) != n, k++); k; } (Perl) use ntheory ":all"; sub a275969 { my(\$k, \$n)=(1, shift); \$k++ while scalar(factor(euler_phi(\$k))) != \$n; \$k; } # Dana Jacobsen, Aug 16 2016 (Perl) use v5.16; use ntheory ":all"; my(\$s, \$chunk, \$lp, @done) = (1, 2e6, 0); while (1) {   my @npf = map { scalar(factor(\$_)) } euler_phi(\$s, \$s+\$chunk-1);   if (vecany { \$_>\$lp } @npf) {     while (my(\$idx, \$val) = each @npf) {       \$done[\$val] //= \$s+\$idx  if \$val > \$lp;     }     while (\$done[\$lp+1]) { \$lp++; say "\$lp \$done[\$lp]"; }   }   \$s += \$chunk; } # Dana Jacobsen, Aug 16 2016 CROSSREFS Cf. A000010, A001222, A019434, A073918. Sequence in context: A128339 A147506 A282960 * A283063 A074854 A284143 Adjacent sequences:  A275966 A275967 A275968 * A275970 A275971 A275972 KEYWORD nonn AUTHOR Altug Alkan, Aug 15 2016 EXTENSIONS a(26)-a(33) from Dana Jacobsen, Aug 16 2016 STATUS approved

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Last modified June 30 19:41 EDT 2022. Contains 354945 sequences. (Running on oeis4.)