A073771 -id:A073771 - cp's OEIS frontend

A135614 Largest highly composite number <= 2*a(n-1).

1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 720, 1260, 2520, 5040, 10080, 20160, 27720, 55440, 110880, 221760, 332640, 665280, 1081080, 2162160, 4324320, 8648640, 17297280, 32432400, 61261200, 122522400, 245044800, 367567200, 735134400, 1396755360, 2793510720, 5587021440

Offset: 1

J. Lowell, Feb 28 2008

nonn

Not the same as A019505; the 29th term of A019505 is 21621600.

			17297280*2 = 34594560; smallest highly composite number <= 34594560 is 32432400.

Michael De Vlieger, Table of n, a(n) for n = 1..3449
Michael De Vlieger, Table of n, position of a(n) in A002182 for n = 1..57930.

Cf. A002182, A073771.

More terms from Jinyuan Wang, Jun 18 2021

A073772 Number of highly composite numbers (HCNs) between the n-th highly composite number k and 2k if 2k is a highly composite number, or -1 if 2*k is not a highly composite number.

Original entry on oeis.org

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

Klaus Brockhaus, Aug 19 2002

sign

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).

			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.

Achim Flammenkamp Highly Composite Numbers.

Cf. A002182, A072938, A073771.

cp's OEIS Frontend

A135614 Largest highly composite number <= 2*a(n-1).

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A073772 Number of highly composite numbers (HCNs) between the n-th highly composite number k and 2k if 2k is a highly composite number, or -1 if 2*k is not a highly composite number.

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cp's OEIS Frontend

A135614 Largest highly composite number <= 2*a(n-1).

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Author

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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.

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A073772 Number of highly composite numbers (HCNs) between the n-th highly composite number k and 2k if 2k is a highly composite number, or -1 if 2*k is not a highly composite number.