A375709 - OEIS

A375709

Numbers k such that A013929(k+1) = A013929(k) + 1. In other words, the k-th nonsquarefree number is 1 less than the next nonsquarefree number.

2, 8, 10, 15, 17, 18, 24, 28, 30, 37, 38, 43, 45, 47, 48, 52, 56, 59, 65, 67, 69, 73, 80, 85, 92, 93, 94, 100, 106, 108, 111, 115, 122, 125, 128, 133, 134, 137, 138, 141, 143, 145, 148, 153, 158, 165, 166, 171, 178, 183, 184, 192, 196, 198, 203, 205, 207, 210

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OFFSET

1,1

COMMENTS

The difference of consecutive nonsquarefree numbers is at least 1 and at most 4, so there are four disjoint sequences of this type:

- A375709 (difference 1) (this)

- A375710 (difference 2)

- A375711 (difference 3)

- A375712 (difference 4)

LINKS

Table of n, a(n) for n=1..58.

FORMULA

Complement of A375710 U A375711 U A375712.

EXAMPLE

The initial nonsquarefree numbers are 4, 8, 9, 12, 16, 18, 20, 24, 25, which first increase by one after the 2nd and 8th terms.

MATHEMATICA

Join@@Position[Differences[Select[Range[100], !SquareFreeQ[#]&]], 1]

CROSSREFS

Positions of 1's in A078147.

For prime-powers (A246655) we have A375734.

First differences are A373409.

For prime numbers we have A375926.

For squarefree instead of nonsquarefree we have A375927.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

A053797 gives lengths of runs of nonsquarefree numbers, firsts A373199.

A375707 counts squarefree numbers between consecutive nonsquarefree numbers.

Cf. A007674, A049094, A061399, A068781, A072284, A110969, A120992, A294242, A373410, A373573.

Sequence in context: A213535 A161349 A336176 * A329952 A073886 A079930

Adjacent sequences: A375706 A375707 A375708 * A375710 A375711 A375712

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 01 2024

STATUS

approved