cp's OEIS Frontend

A253266 Numbers such that the minimum distance between divisors of n occurs only between composite numbers.

%I A253266 #10 May 02 2015 11:15:43
%S A253266 14399,34595,82943,89999,100793,116963,158389,172975,224675,244783,
%T A253266 245021,266255,278783,281957,285155,304703,331177,338723,343387,
%U A253266 380545,417571,446369,447557,484415,497021,532763,580601,585221,588115,590359,608399,619157,627263,629993
%N A253266 Numbers such that the minimum distance between divisors of n occurs only between composite numbers.
%C A253266 All members of the sequence are either a square minus a small square, or a multiple of a smaller member of the sequence. The square root of the small square must be less than half the fourth root of the number.
%C A253266 245021 is the smallest member of this sequence that is neither 1 less than a square nor a multiple of a smaller member of the sequence. It is 4 less than a square.
%H A253266 Franklin T. Adams-Watters, <a href="/A253266/a253266.txt">Proof of assertion</a>
%e A253266 The divisors of 14399 = 119*121 are 1, 7, 11, 17, 77, 119, 121, 187, 847, 1309, 2057, 14399. The minimum difference between divisors is 2, which occurs only between 119 and 121, both of which are composite; so 14399 is in the sequence.
%e A253266 The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. The minimum difference is 1, which does occur between two composites - 8, 9 - but it also occurs between pairs not both composite (e.g. 1, 2 or 3, 4), so 72 is not in the sequence.
%o A253266 (PARI) isa(n) = local(ds=divisors(n),diff,mind,dcomp);mind=n;for(k=2,#ds,diff=ds[k]-ds[k-1];if(diff<=mind,if(diff<mind,mind=diff;dcomp=1);if(isprime(ds[k])||isprime(ds[k-1]),dcomp=0)));dcomp
%Y A253266 Cf. A060680 (minimum difference), A033676 and A033677 (central divisors).
%K A253266 nonn
%O A253266 1,1
%A A253266 _Franklin T. Adams-Watters_, May 01 2015