[seqfan] A137921 & "divisor Islands"

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Sun Feb 7 18:38:14 CET 2010

Regarding A137921: First, by d, does the author mean only PROPER divisors?
Are there other sequences in the database where "proper divisor" should have been included in the title or in a comment, instead of simply "divisor" (so as to avoid confusion)?

By the way, with "divisor" of n interpreted to include n itself, then we have A137921 equal to this sequence I just submitted (but not yet appearing):

%I A175102
%S A175102 1,1,2,2,2,2,2,3,3,3,2,3,2,3,4,4,2,4,2,4,4
%N A175102 a(n) = number of "divisor islands" of n. A divisor island is any set of consecutive divisors of a number where no pairs of consecutive divisors in the set are separated by 2 or more. 
%e A175102 The divisors of 30 are 1,2,3,5,6,10,15,30. The divisor islands are (1,2,3), (5,6), (10), (15), (30). (Note that the differences between consecutive divisors 5-3, 10-6, 15-10, and 30-15 are all > 1.) There are 5 such islands, so a(30)=5. 
%K A175102 more,nonn
%O A175102 1,3

I should have included a cross-ref to A137921, but I did not want to do that until the title of A137921 is fixed.

Leroy Quet

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