A367949 - OEIS

A367949

Lexicographically earliest sequence of distinct positive integers such that the sum of the distinct prime factors (sopf) of a(n) + a(n + 1) is a perfect square.

1, 13, 15, 24, 4, 10, 18, 21, 7, 32, 14, 25, 3, 11, 17, 22, 6, 8, 20, 19, 9, 5, 23, 16, 12, 2, 26, 29, 27, 28, 38, 54, 40, 52, 42, 50, 44, 48, 46, 66, 51, 41, 53, 39, 55, 37, 57, 35, 31, 61, 33, 59, 58, 34, 60, 72, 45, 47, 65, 67, 88, 70, 62, 30, 36, 56, 76, 79, 104, 80

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..70.

Éric Angelini, Sums of distinct prime factors, Personal blog, December 2023.

EXAMPLE

a(1) + a(2) = 1 + 13 = 14 whose sopf is 9, a perfect square.

a(2) + a(3) = 13 + 15 = 28 whose sopf is 9, a perfect square.

a(7) + a(8) = 18 + 21 = 39 whose sopf is 16, a perfect square.

a(8) + a(9) = 21 + 7 = 28 whose sopf is 9, a perfect square.

MATHEMATICA