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 A284168 Integers n such that sigma(binomial(n,k)) = sigma(binomial(n-1,k-1)) + sigma(binomial(n-1,k)) for some k. 1
 3, 6, 15, 25, 27, 30, 35, 40, 48, 50, 54, 60, 63, 66, 78, 80, 100, 108, 112, 118, 120, 123, 124, 126, 140, 144, 158, 175, 192, 198, 200, 207, 216, 220, 224, 225, 232, 238, 243, 247, 304, 310, 316, 319, 341, 345, 348, 358, 364, 368, 375, 385, 391, 408, 416, 425, 432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Consider the triangle formed by replacing each m in Pascal's triangle with sigma(m). Then this sequence consists of the row indices where there is a term that is equal to the sum of its NW and N neighbors as in a Pascal triangle. LINKS EXAMPLE Here is the triangle also described in A074801. 1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 7, 12, 7, 1, 1, 6, 18, 18, 6, 1, On row index 3, we have 4 which is the sum of 1 and 3 its NW and N neighbors. So a(1)= 3, and its column index is 1 which will be corresponding value in A284169. PROG (PARI) T(n, k) = sigma(binomial(n, k)); isokT(n, k) = T(n-1, k-1) + T (n-1, k) == T(n, k); isokn(n) = for (k=1, n-1, if (isokT(n, k), return(1))); CROSSREFS Cf. A000203, A007318, A074801, A284169. Sequence in context: A286502 A287101 A287189 * A216304 A020991 A079825 Adjacent sequences:  A284165 A284166 A284167 * A284169 A284170 A284171 KEYWORD nonn AUTHOR Michel Marcus, Mar 21 2017 STATUS approved

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Last modified December 11 17:59 EST 2019. Contains 329925 sequences. (Running on oeis4.)