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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

Table of n, a(n) for n=1..33.

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 July 5 23:36 EDT 2020. Contains 335475 sequences. (Running on oeis4.)