id:A068067 - OEIS Search Results

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Number of integers m, 0 < m <= n, such that n divides m(m+1)/2.

+0
2

1, 0, 2, 0, 2, 1, 2, 0, 2, 1, 2, 1, 2, 1, 4, 0, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 0, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 4, 1, 2, 3, 2, 1, 4, 0, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 4, 1, 4, 3, 2, 1, 2, 1, 2, 3, 4, 1, 4, 1, 2, 3, 4, 1, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 1, 8 (list; graph; listen)

	OFFSET	`1,3`
	COMMENT	`a(n) = 0 iff n = 2^k with k >= 1.` `Least n with a(n) = 2^k is p(k+1)#/2 = A002110(A000040(k+1))/2. Least n with a(n) = 2^k-1 != 1 is p(k+1)#.`
	FORMULA	`If n is even, a(n) = 2^(omega(n)-1) - 1; if n is odd, a(n) = 2^omega(n). Here omega(n) = A001221(n) is the number of distinct prime divisors of n.`
	MATHEMATICA	`a[n_] := Length[Select[Range[n], Mod[ #(#+1)/2, n]==0&]]`
	CROSSREFS	`Cf. A068068(n)-a(n) = 0 if n is odd, 1 if n is even.` `Sequence in context: A068907 A033687 A133457 this_sequence A046926 A074398 A070824` `Adjacent sequences: A068064 A068065 A068066 this_sequence A068068 A068069 A068070`
	KEYWORD	`nonn`
	AUTHOR	`Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 18 2002`
	EXTENSIONS	`Edited by David W. Wilson (davidwwilson(AT)comcast.net) and Dean Hickerson (dean(AT)math.ucdavis.edu), Jun 08 2002`

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Last modified September 5 01:44 EDT 2008. Contains 143476 sequences.

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