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Numbers in whose prime factorization the indices of primes do not sum to a triangular number.
4

%I #10 Sep 13 2015 07:43:44

%S 3,4,7,9,10,11,12,14,15,16,17,18,19,20,23,24,26,31,32,33,34,35,37,38,

%T 39,41,42,43,44,45,49,50,51,52,53,54,55,56,58,59,60,61,62,63,65,66,67,

%U 68,69,70,71,72,74,75,77,78,79,80,81,82,83,84,87,88,89,90,92,93,94,95,96,97,98,99,100

%N Numbers in whose prime factorization the indices of primes do not sum to a triangular number.

%C Numbers k such that A010054(A056239(k)) is zero, or equally, such that A002262(A056239(k)) is not zero.

%C These are numbers such that any iterations of A242424 started from them lead eventually to a cycle greater than one. Please see the comments and references at A242422.

%H Antti Karttunen, <a href="/A242423/b242423.txt">Table of n, a(n) for n = 1..27575</a>

%e 3 = p_2 is present, because 2 is not a triangular number.

%e 4 = p_1 * p_1 is present, because 1+1 = 2 is not a triangular number.

%o (Scheme, with _Antti Karttunen_'s Intseq-library)

%o (define A242423 (ZERO-POS 1 1 (COMPOSE A010054 A056239)))

%Y Complement: A242422.

%Y Cf. A215366, A242424, A000217, A002262, A010054, A056239.

%K nonn

%O 1,1

%A _Antti Karttunen_, May 16 2014