

A281627


a(n) is the smallest number k such sigma(phi(k)) = A062402(k) is the nth Mersenne prime (A000668(n)), or 0 if no such k exists.


1




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 = 118; 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<nexists(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



