A088725 - OEIS

A088725

Numbers having no divisors d>1 such that also d+1 is a divisor.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Complement of A088723.

Union of A132895 and A005408, the odd numbers. - Ray Chandler, May 29 2008

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 9, 79, 778, 7782, 77813, 778055, 7780548, 77805234, 778052138, 7780519314, ... . Apparently, the asymptotic density of this sequence exists and equals 0.77805... . - Amiram Eldar, Jun 14 2022

LINKS

Table of n, a(n) for n=1..72.

FORMULA

A088722(a(n)) = 0.

EXAMPLE

From Gus Wiseman, Oct 16 2019: (Start)

The sequence of terms together with their divisors > 1 begins:

1: {}

2: {2}

3: {3}

4: {2,4}

5: {5}

7: {7}

8: {2,4,8}

9: {3,9}

10: {2,5,10}

11: {11}

13: {13}

14: {2,7,14}

15: {3,5,15}

16: {2,4,8,16}

17: {17}

19: {19}

21: {3,7,21}

22: {2,11,22}

23: {23}

25: {5,25}

(End)

MATHEMATICA

Select[Range[100], FreeQ[Differences[Rest[Divisors[#]]], 1]&] (* Harvey P. Dale, Sep 16 2017 *)

PROG

(PARI) isok(n) = {my(d=setminus(divisors(n), [1])); #setintersect(d, apply(x->x+1, d)) == 0; } \\ Michel Marcus, Oct 28 2019

CROSSREFS

Positions of 0's and 1's in A129308.

Positions of 0's and 1's in A328457 (also).

Numbers whose divisors (including 1) have no non-singleton runs are A005408.

The number of runs of divisors of n is A137921(n).

The longest run of divisors of n has length A055874(n).

Cf. A000005, A027750, A060680, A088722, A088723 (complement), A088724, A088726, A328166, A328450.

Sequence in context: A350838 A364347 A228869 * A094520 A136447 A005100

Adjacent sequences: A088722 A088723 A088724 * A088726 A088727 A088728

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 12 2003

EXTENSIONS

Extended by Ray Chandler, May 29 2008

STATUS

approved