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A281627 a(n) is the smallest number k such 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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=1..8.

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. A062402, A062514.

Cf. A002181, A002202, A023194.

Cf. A053576 (includes the first 8 known terms of this sequence).

Sequence in context: A232238 A102295 A227335 * A102846 A100003 A283331

Adjacent sequences:  A281624 A281625 A281626 * A281628 A281629 A281630

KEYWORD

nonn,more

AUTHOR

Jaroslav Krizek, Feb 11 2017

EXTENSIONS

a(8) from Michel Marcus, Feb 12 2017

STATUS

approved

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Last modified September 18 22:25 EDT 2020. Contains 337174 sequences. (Running on oeis4.)