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A291138 a(n) is the smallest k such that psi(k) and phi(k) have same distinct prime factors when k is the product of n distinct primes (psi(k) = A001615(k) and phi(k) = A000010(k)), or 0 if no such k exists. 0
3, 14, 42, 210, 3570, 43890, 746130, 14804790, 281291010, 8720021310 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

a(5) = 3570 = 2*3*5*7*17 because psi(3570) = 3*4*6*8*18 = 2^7*3^4, and phi(3570) = 2*4*6*16 = 2^8*3^1 and 3570 is the least number with 5 distinct prime factors having this property.

MATHEMATICA

Rest@ Values[#][[All, 1]] &@ KeySort@ PositionIndex@ Table[If[SameQ @@ #, PrimeNu@ n, 0] &@ Map[FactorInteger[#][[All, 1]] &, {EulerPhi@ n, n Sum[MoebiusMu[d]^2/d, {d, Divisors@ n}]}], {n, 10^6}] (* Michael De Vlieger, Aug 26 2017, after Michael Somos at A001615 *)

CROSSREFS

Cf. A000010 (phi), A005117 (squarefree), A001615 (psi), A007947 (radical).

Sequence in context: A055650 A000550 A124650 * A063903 A305009 A115005

Adjacent sequences:  A291135 A291136 A291137 * A291139 A291140 A291141

KEYWORD

nonn,more

AUTHOR

Altug Alkan, Aug 18 2017

EXTENSIONS

a(10) from Giovanni Resta, Aug 26 2017

STATUS

approved

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Last modified June 14 21:25 EDT 2021. Contains 345040 sequences. (Running on oeis4.)