A158976 -id:A158976 - cp's OEIS frontend

A158978 a(n) = product of numbers k <= n such that not all proper divisors of k are divisors of n.

1, 1, 1, 1, 4, 1, 24, 6, 192, 432, 17280, 10, 207360, 51840, 322560, 1360800, 696729600, 3225600, 12541132800, 39191040, 27869184000, 1316818944000, 115880067072000, 349272000, 2781121609728000, 17382010060800000

Offset: 1

Jaroslav Krizek, Apr 01 2009

nonn

The empty product is 1.

For primes p, a(p) = A000142(p) / A034386(p).

			For n = 7 we have the following proper divisors of k <= n: {1}, {1}, {1}, {1, 2}, {1}, {1, 2, 3}, {1}. Only 4 and 6 have proper divisors that are not divisors of 7, viz. 2 and 2, 3. Hence a(7) = 4 * 6 = 24.

Cf. A000040, A000142, A034386, A158976.

[ IsEmpty(S) select 1 else &*S where S is [ k: k in [1..n] | exists(t){ d: d in Divisors(k) | d ne k and d notin Divisors(n) } ]: n in [1..26] ];

Edited and extended by Klaus Brockhaus, Apr 07 2009

A159074 Sum of the k in the range 1<=k<=n such that set of proper divisors of k is not a subset of the set of proper divisors of n.

Original entry on oeis.org

1, 1, 1, 1, 5, 1, 11, 7, 19, 24, 38, 11, 50, 46, 55, 67, 95, 76, 113, 91, 124, 150, 176, 121, 200, 221, 242, 252, 306, 237

Offset: 1

Jaroslav Krizek, Apr 04 2009

nonn

The nomenclature of A159072 applies, where the terms in that sum are counted.

			a(8) = 7 adds k = 6, where {1, 2, 3} is not a subset of the divisor set {1, 2, 4} of n = 8, and k = 1, with an empty proper divisor set.

Cf.: A158976, A000217, A000040, A014284, A036234.

a(n) = A158976(n) + 1.
If p = prime, a(p) = A000217(p) - A158662(p) + 1 = A000217(p) - A014284[A036234(p)] + 1.
a(n)+A159073(n)=A000217(n). - R. J. Mathar, Apr 06 2009

Edited by R. J. Mathar, Apr 06 2009

cp's OEIS Frontend

A158978 a(n) = product of numbers k <= n such that not all proper divisors of k are divisors of n.

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