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A381901 Partition the natural numbers by letting a(1)=1 (denoting the set {1}) and for n>1 define a(n) to be the least integer such that the product of the set of integers {a(n-1)+1,...,a(n)} is an integer multiple of the previous partition's product.

%I A381901 #17 Apr 13 2025 17:42:14
%S A381901 1,2,4,8,14,26,46,86,166,326,634,1262,2518,5006,10006,19946,39874,
%T A381901 79738,159398,318778,637502,1274998,2549978,5099902,10199786,20399534,
%U A381901 40799062,81598082,163196134,326392258,652784498,1305568942,2611137838,5222275634,10444551254
%N A381901 Partition the natural numbers by letting a(1)=1 (denoting the set {1}) and for n>1 define a(n) to be the least integer such that the product of the set of integers {a(n-1)+1,...,a(n)} is an integer multiple of the previous partition's product.
%F A381901 a(n) = A090905(n+1) - 1.
%F A381901 a(n) = 2 * A006992(n-1) for n>=5.
%e A381901 The first few corresponding partitions are {1}, {2}, {3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12, 13, 14}.
%Y A381901 Cf. A006992, A090905.
%Y A381901 Appears to agree with A113117 starting at the 5th term and with A113118 starting at the 6th term.
%K A381901 nonn
%O A381901 1,2
%A A381901 _Andy Niedermaier_, Mar 09 2025