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A263810 Numbers n such that n = tau(n) * phi(n-2) + 1. 1
3, 4, 5, 17, 257, 65537, 83623937 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that n = A000005(n) * A000010(n-2) + 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(n-2) + 1 then phi(n-2) must divide n-1, thus n-2 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(n-2) + 1]

(PARI) for(n=3, 1e8, if(numdiv(n)*eulerphi(n-2) == n-1, print1(n ", "))) \\ Altug Alkan, Oct 28 2015

(PARI) lista(na, nb) = {my(f1 = factor(na-2), f2 = factor(na-1), f3); for(n=na, nb, f3 = factor(n); if (numdiv(f3)*eulerphi(f1) == n-1, 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(n-1) + 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

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Last modified June 7 01:26 EDT 2020. Contains 334836 sequences. (Running on oeis4.)