

A088725


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


18



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
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OFFSET

1,2


COMMENTS

A088722(a(n))=0; complement of A088723.
Union of A132895 and A005408, the odd numbers.  Ray Chandler, May 29 2008


LINKS

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


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 nonsingleton 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: A023800 A320340 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



