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A073772
Number of highly composite numbers (HCNs) between the n-th highly composite number k and 2*k if 2*k is a highly composite number, or -1 if 2*k is not a highly composite number.
0
0, 0, -1, 0, 0, 1, -1, -1, 0, 1, 1, -1, 0, -1, 1, 1, -1, 0, 1, 1, 1, -1, -1, 2, 2, -1, -1, 1, 1, 1, 2, -1, 2, 2, -1, -1, -1, 1, 1, 1, 2, -1, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, 2, -1, 2, 2, -1, 2, 2, 2, -1, -1, 2, 2, 2, -1, 2, 3, -1, -1, 2, 2, 2, -1, -1, 1, 1, 1, 1, -1, -1, 3, 3, 3, 3, -1, -1, 2, 2, 2, -1, 1, 1, -1, 3, 3, 3, 3
OFFSET
1,24
COMMENTS
If 2*A002182(n) = A002182(m) then a(n) = m - n - 1; if 2*A002182(n) is not a highly composite number then a(n) = -1. The zero terms correspond to the terms of A072938, the negative terms correspond to the terms of A073771. The terms were determined by means of A. Flammenkamp's list (cf. Links).
EXAMPLE
a(3) = -1 since 4 is the third highly composite number and 2*4 = 8 is not a highly composite number; a(6) = 1 since 24 is the sixth highly composite number, 2*24 = 48 is the eighth highly composite number and the highly composite number 36 is between them; a(13) = 0 since 360 is the 13th highly composite number, 2*360 = 720 is the 14th highly composite number and there is no highly composite number between them.
CROSSREFS
KEYWORD
sign
AUTHOR
Klaus Brockhaus, Aug 19 2002
STATUS
approved