

A263810


Numbers n such that n = tau(n) * phi(n2) + 1.


1




OFFSET

1,1


COMMENTS

Numbers n such that n = A000005(n) * A000010(n2) + 1.
Sequence deviates from A249541; numbers 4294967297 and 6992962672132097 are not terms of this sequence.
The first 5 known Fermat primes from A019434 are in sequence.
Conjecture: primes from this sequence are in A254576.
a(8) > 10^13. If n = tau(n) * phi(n2) + 1 then phi(n2) must divide n1, thus n2 must be a term of A203966, which has already been searched up to 10^13.  Giovanni Resta, Feb 21 2020


LINKS

Table of n, a(n) for n=1..7.


EXAMPLE

17 is in this sequence because 17 = tau(17)*phi(15)+1 = 2*8+1.


MATHEMATICA

Select[Range@ 100000, # == DivisorSigma[0, #] EulerPhi[#  2] + 1 &] (* Michael De Vlieger, Oct 27 2015 *)


PROG

(MAGMA) [n: n in [3..1000000]  n eq NumberOfDivisors(n) * EulerPhi(n2) + 1]
(PARI) for(n=3, 1e8, if(numdiv(n)*eulerphi(n2) == n1, print1(n ", "))) \\ Altug Alkan, Oct 28 2015
(PARI) lista(na, nb) = {my(f1 = factor(na2), f2 = factor(na1), f3); for(n=na, nb, f3 = factor(n); if (numdiv(f3)*eulerphi(f1) == n1, print1(n ", ")); f1 = f2; f2 = f3; ); }; \\ Michel Marcus, Feb 21 2020


CROSSREFS

Cf. A000005, A000010, A019434, A249541, A254576, A203966.
Cf. A263811 (numbers n such that n = tau(n) * phi(n1) + 1).
Sequence in context: A173061 A174326 A224890 * A249541 A059184 A161961
Adjacent sequences: A263807 A263808 A263809 * A263811 A263812 A263813


KEYWORD

nonn,more


AUTHOR

Jaroslav Krizek, Oct 27 2015


STATUS

approved



