A394866 a(1) = 1; for n > 1, a(n) is the number of integers m in [2^(n-1)..3^(n-1) - 1] such that A000005(m) = n.

1, 1, 1, 7, 1, 27, 1, 408, 19, 254, 1, 17091, 1, 3074, 191, 2060123, 1, 725434, 1, 13590448, 1380, 693870, 1, 7021506649, 194, 11557671, 341926, 15572577478, 1, 50062082037, 1, 69848972741943, 121055, 3524329794, 1538, 330291266156667, 1, 63367446007, 1289195

Offset

1,4

Comments

a(n) = 1 if n is a noncomposite number (A008578) and a(n) > 1 if n is a composite number (A002808).

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\ | | | | | | | | | | |

\ with only tau = | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

--------------- | | | | | | | | | | |

bounds on \ | | | | | | | | | | |

the region = \| | | | | | | | | | |

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1..2^(n-1)-1 | 0 | 0 | 0 | 1 | 0 | 4 | 0 | 15 | 4 | 12 | A393179(n)-1

2^(n-1)..3^(n-1)-1 | 1 | 1 | 1 | 7 | 1 | 27 | 1 | 408 | 19 | 254 | a(n)

3^(n-1)..5^(n-1)-1 | 0 | | | | | | | | | |

5^(n-1)..7^(n-1)-1 |...|...|...| ... |...| ... |...| ... | ... | ... |

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A390951 A394226 A395379 A395380 A395381

Links

Table of n, a(n) for n=1..39.

Example

a(1) = 1 because only contains 1 integer 1 such that A000005(m) = 1;
a(2) = 1 because [2..2] contains 1 integer 2 such that A000005(m) = 2;
a(3) = 1 because [4..8] contains 1 integer 4 such that A000005(m) = 3;
a(4) = 7 because [8..26] contains 7 integers 8, 10, 14, 15, 21, 22, 26 such that A000005(m) = 4.

Mathematica

a[n_] := If[CompositeQ[n], Sum[Boole[DivisorSigma[0, k] == n], {k, 2^(n-1), 3^(n-1)-1}], 1]; Array[a, 15] (* Amiram Eldar, May 07 2026 *)

Prog

(Magma) [1] cat [#[m: m in [2^(n-1)..3^(n-1) - 1] | #Divisors(m) eq n]: n in [2..10]];
(PARI) a(n) = if (n==1, 1, my(nb=0); forfactored(f=2^(n-1), 3^(n-1)-1, if(numdiv(f[2])==n, nb++)); nb); \\ Michel Marcus, May 07 2026

Crossrefs

Cf. A000079, A024023.

Cf. A000005, A002808, A008578.

Cf. A390951, A394226, A395379, A395380, A395381.

Sequence in context: A183109 A082172 A053288 * A282917 A050301 A146996

Adjacent sequences: A394863 A394864 A394865 * A394867 A394868 A394869

Keyword

nonn

Author

Juri-Stepan Gerasimov, May 02 2026

Extensions

a(18)-a(19) from Michel Marcus, May 07 2026

a(20)-a(23) from Amiram Eldar, May 07 2026

a(24)-a(39) from Daniel Suteu, May 25 2026

Status

approved