

A064234


The least k such that A063994(k) = Product_{primes p dividing k} gcd(p1, k1) = n, or 0 if there's no such k.


2



1, 3, 28, 5, 66, 7, 232, 45, 190, 11, 276, 13, 1106, 0, 286, 17, 1854, 19, 3820, 891, 2752, 23, 1128, 595, 2046, 0, 532, 29, 1770, 31, 9952, 425, 1288, 0, 2486, 37, 8474, 0, 742, 41, 3486, 43, 7612, 5589, 2356, 47, 13584, 325, 9850, 0, 20554, 53, 5778, 0, 12926, 435, 13282, 59, 42540, 61
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OFFSET

1,2


COMMENTS

From Richard N. Smith, Jul 15 2019: (Start)
The comment in the "Mathematica" section is not true: A063994(65513) = 76 (thus a(76) = 65513 instead of 0), but 76 is an even nontotient (in the sequence A005277).
The first counterexample of the comment is A063994(1541) = 484, which is an even nontotient, for the counterexamples <= 2^20, see the link.
Also A063994(1072871) = 68. (thus a(68) = 1072871).
Conjecture: a(n) = 0 iff n == 2 mod 4 and n+1 is composite, if this conjecture is true, then a(54), a(110), a(294), etc. would be 0.
Another conjecture: If A063994(k) = n and n == 2 mod 4, then n+1 is prime and k is a power of n+1. (End)


LINKS

Richard N. Smith, Table of n, a(n) for n = 1..187
Richard N. Smith, Numbers n such that A063994(n) is an even nontotient (format: n,A063994(n))


MATHEMATICA

f[ n_ ] := If[ n == 1, 1, Apply[ Times, GCD[ n  1, Transpose[ FactorInteger[ n ] ] [ [ 1 ] ]  1 ] ] ]; a = Table[ 0, {100} ]; Do[ m = f[ n ]; If[ m < 101 && a[ [ m ] ] == 0, a[ [ m ] ] = n ], {n, 1, 10^7} ]; a a(54) > 2*10^7. The zeros appear at positions that are the values in the sequence A005277, the nontotients: even n such that phi(m) = n has no solution. [Warning: This is wrong, see the "comment" section]


PROG

(PARI) a063994(n)=my(f=factor(n)[, 1]); prod(i=1, #f, gcd(f[i]1, n1))
a(n)=if(n%4==2 && !isprime(n+1), 0, for(k=1, 2^30, if(a063994(k)==n, return(k)))) \\ Richard N. Smith, Jul 15 2019, after Charles R Greathouse IV in A063994


CROSSREFS

Cf. A063994, A005277, A002202, A049225, A254139.
Sequence in context: A162414 A188927 A146072 * A224579 A037102 A042169
Adjacent sequences: A064231 A064232 A064233 * A064235 A064236 A064237


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Sep 22 2001


EXTENSIONS

a(54)  a(60) from Richard N. Smith, Jul 15 2019


STATUS

approved



