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A281627
a(n) is the smallest number k such that sigma(phi(k)) = A062402(k) is the n-th Mersenne prime (A000668(n)), or 0 if no such k exists.
1
3, 5, 17, 85, 4369, 65537, 327685, 1431655765
OFFSET
1,1
COMMENTS
Conjecture 1: If A062402(n) = A000203(A000010(n)) = sigma(phi(n)) is a prime p for some n, then p is Mersenne prime (A000668); a(n) > 0 for all n.
Conjecture 2: a(n) = the smallest number k such that phi(k) has exactly A000043(n)-1 divisors; see A276044.
Conjecture 3: a(n) = the smallest number k such that phi(k) has exactly A000043(n)-1 prime factors (counted with multiplicity); see A275969.
a(n) <= A000668(n) for n = 1-18; conjecture: a(n) <= A000668(n) for all n.
Equals A002181(index in A002202 of (intersection of A023194 and A002202)). - Michel Marcus, Feb 12 2017
PROG
(Magma) A281627:=func<n|exists(r){k:k in[1..1000000] | SumOfDivisors(EulerPhi(k)) eq n}select r else 0>; Set(Sort([A281627(n): n in [SumOfDivisors(EulerPhi(n)): n in[1..1000000] | IsPrime(SumOfDivisors(EulerPhi(n)))]]))
(PARI) terms() = {v = readvec("b023194.txt"); for(i=1, #v, if (istotient(v[i], &n), print1(n/2, ", ")); ); } \\ Michel Marcus, Feb 12 2017
CROSSREFS
Cf. A053576 (includes the first 8 known terms of this sequence).
Sequence in context: A365518 A227335 A351718 * A102846 A100003 A283331
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Feb 11 2017
EXTENSIONS
a(8) from Michel Marcus, Feb 12 2017
STATUS
approved