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 A167766 Minimum numbers whose phi of phi are multiples of the n-th prime: the n-th term is the minimum integer x such that: prime(n) | phi(phi(x)), prime(n) being the n-th prime. 3
 5, 19, 23, 59, 47, 107, 479, 383, 283, 467, 1367, 1187, 167, 347, 1319, 643, 2837, 2203, 2153, 3413, 587, 5693, 1997, 359, 5827, 1619, 2063, 2999, 4799, 3167, 1019, 1579, 5483, 3343, 7159, 3023, 12569, 1307, 4679, 2083, 719, 3623, 4597, 3863, 18917, 4783 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These minimal integers are always prime. To be clear, the phi function referred to here is Euler's totient function. LINKS Donovan Johnson, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Euler's Totient Function EXAMPLE The first term is 5. phi(5) = 4 and phi(4)=2. 2 is a multiple of the first prime 2. 5 is the lowest such number x where 2 divides phi(phi(x)). MAPLE with(numtheory): P:=proc(n) local a, k; a:=ithprime(n); for k from 1 to 10^3 do if frac(phi(phi(ithprime(k)))/a)=0 then RETURN(ithprime(k)); break; fi; od; end: seq(P(i), i=1..46); # Paolo P. Lava, Oct 10 2018 MATHEMATICA a[n_] := (p=Prime[n]; k=1; While[k++; x=Prime[k]; Mod[ EulerPhi[ EulerPhi[x]], p] != 0]; x); Table[a[n], {n, 50}] (* Jean-François Alcover, Sep 14 2011 *) PROG (PARI) /* not the most efficient implementation */ ppp(a, b)= { forprime(p=a, b, v = 2*p + 1; v2 = 1; minv = 100000000; while (v2 <= minv || v <=minv, /* print ("Checking ", v, " for ", p); */ while(!isprime(v), v += 2*p /*; print ("Checking ", v, " for ", p)*/ ); if (v%(p*p)==1, /* don't do this step if: p^2 | v-1 */ v2 = v , v2 = 2*v + 1; while (!isprime(v2) && v2 < minv, v2 += 2*v ) ); if (v2 < minv, minv = v2; ); v += 2*p ); print (p, " => ", minv) ) } CROSSREFS Cf. A010554. Sequence in context: A191084 A146509 A062340 * A106957 A236167 A022143 Adjacent sequences:  A167763 A167764 A167765 * A167767 A167768 A167769 KEYWORD easy,nice,nonn AUTHOR Fred Schneider, Nov 11 2009 STATUS approved

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Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)