A337158 a(n) is the start m of first run of n consecutive numbers with periodic sequence of values of number of divisors [tau(m), tau(m+1), tau(m), tau(m+1), tau(m), ...] where tau(m) != tau(m+1).

1, 1, 3, 5, 182, 182, 4853, 445145, 6139163, 55804443, 55804443, 856530193, 856530193, 7709802455641

Offset

1,3

Comments

Sequences of starts of runs of n consecutive numbers m with this property:

n = 1: A000027

n = 2: 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, ...

n = 3: 3, 5, 6, 8, 11, 17, 18, 29, 40, 41, 50, 54, 55, 59, 71, ...

n = 4: 5, 17, 40, 54, 101, 136, 182, 183, 184, 197, 246, 247, ...

n = 5: 182, 183, 246, 339, 413, 469, 470, 533, 1203, 1312, 1313, ...

n = 6: 182, 469, 1312, 4853, 4854, 9052, 13701, 19164, 24347, ...

n = 7: 4853, 37909, 47644, 50467, 62885, 106517, 117605, 126181, ...

n = 8: 445145, 3226845, 3648543, 4651846, 5763545, 6139163, ...

n = 9: 6139163, 10371544, 13714143, 18278045, ...

Links

Table of n, a(n) for n=1..14.

Example

[tau(5), tau(6), tau(7), tau(8)] = [2, 4, 2, 4].
[tau(182), tau(183), tau(184), tau(185), tau(186), tau(187)] = [8, 4, 8, 4, 8, 4].

Crossrefs

Cf. A000005 (tau), A006558.

Sequence in context: A038535 A090953 A092947 * A333413 A104996 A211767

Adjacent sequences: A337155 A337156 A337157 * A337159 A337160 A337161

Keyword

nonn,more

Author

Jaroslav Krizek, Jan 28 2021

Extensions

a(10)-a(13) from Amiram Eldar, Jan 28 2021

a(14) from Martin Ehrenstein, Feb 08 2021

Status

approved