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 A346094 a(n) = n / A275823(n), where A275823(n) is the least k such that n divides phi(k^2). 1
 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 6, 5, 2, 3, 2, 1, 4, 1, 2, 3, 4, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 4, 3, 2, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS a(n) = n divided by the least k such that A002618(k) [= phi(k^2) = k*phi(k)] is a multiple of n. It is easy to see that such k is always a divisor of n since k contains only some of prime factors of n and there cannot be other prime factor that does not divide n. In order to see this, let us assume p divides k (where p is prime that does not divide n) and (p-1) contribute the division in A275823. At this case there is definitely smaller option to do this instead of p-1 since it is always possible that k could contain necessary prime powers from factorization of p-1 instead of p. At the same time, obviously A275823(n) <= n. So terms of this sequence are always integers. LINKS MATHEMATICA Array[#/Block[{k = 1}, While[! Mod[EulerPhi[k^2], #] == 0, k++]; k] &, 105] (* Michael De Vlieger, Jul 22 2021 *) PROG (PARI) A346094(n) = { my(k=1); while((k*eulerphi(k)) % n, k++); (n/k); }; CROSSREFS Cf. A002618, A275823. Sequence in context: A161305 A161280 A160984 * A082898 A095999 A334948 Adjacent sequences: A346091 A346092 A346093 * A346095 A346096 A346097 KEYWORD nonn AUTHOR Antti Karttunen and Altug Alkan, Jul 21 2021 STATUS approved

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Last modified March 31 00:51 EDT 2023. Contains 361623 sequences. (Running on oeis4.)