A072938 -id:A072938 - cp's OEIS frontend

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.

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

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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.

A160274 Highly composite numbers A002182(n) with the property that A002182(n+1)/A002182(n) >= A002182(k+1)/A002182(k) for all k>n.

Original entry on oeis.org

1, 2, 6, 12, 60, 360, 2520

Offset: 1

Anonymous, May 07 2009

			2520 is a term of this sequence because 2520 is a highly composite number (A002182(18)), A002182(19)/A002182(18) = 2, and 2 >= A002182(k+1)/A002182(k) for all k>18. (In fact, 2 > A002182(k+1)/A002182(k) for all k>18.)

Cf. A002182, A002201, A072938, A106037, A094348, A003418, A002110.

cp's OEIS Frontend

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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A160274 Highly composite numbers A002182(n) with the property that A002182(n+1)/A002182(n) >= A002182(k+1)/A002182(k) for all k>n.

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cp's OEIS Frontend

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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Author

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Examples

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A160274 Highly composite numbers A002182(n) with the property that A002182(n+1)/A002182(n) >= A002182(k+1)/A002182(k) for all k>n.

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Crossrefs

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.