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

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Last modified May 9 06:30 EDT 2021. Contains 343692 sequences. (Running on oeis4.)