A087061 -id:A087061 - cp's OEIS frontend

A087036 Lunar cubes: nnn, where * is lunar multiplication.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1000, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 2000, 2111, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 3000, 3111, 3222, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 4000, 4111, 4222, 4333, 4444, 4445, 4446, 4447

Offset: 0

Marc LeBrun and N. J. A. Sloane, Oct 19 2003

nonn

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

A087051 Lunar fourth powers: nnnn, where is lunar multiplication.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10000, 11111, 11112, 11113, 11114, 11115, 11116, 11117, 11118, 11119, 20000, 21111, 22222, 22223, 22224, 22225, 22226, 22227, 22228, 22229, 30000, 31111, 32222, 33333, 33334, 33335, 33336, 33337, 33338, 33339, 40000, 41111, 42222

Offset: 0

Marc LeBrun and N. J. A. Sloane, Oct 19 2003

nonn

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

A088473 Numbers n such that the lunar sum of the distinct lunar prime divisors of n is <= n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139

Offset: 1

David Applegate, Nov 11 2003

nonn

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Index entries for sequences related to dismal (or lunar) arithmetic

A088475 Numbers n such that the lunar sum of the distinct lunar prime divisors of n is >= n.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset: 1

David Applegate, Nov 11 2003

			The only lunar prime that divides 10 is 90: 90*1 = 10 (cf. A087061, A087062, A087097) and 90 >= 10, so 10 is a member. - _N. J. A. Sloane_, Mar 04 2007, corrected Oct 07 2010.

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Tanya Khovanova, Non Recursions
Index entries for sequences related to dismal (or lunar) arithmetic

Complement is A088472, which starts 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 110, 112, ...

Definition made more precise by Marc LeBrun, Mar 04 2007

A088476 Numbers n such that the lunar sum of the distinct lunar prime divisors of n is > n.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82

Offset: 1

David Applegate, Nov 11 2003

nonn

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Index entries for sequences related to dismal (or lunar) arithmetic

A088477 Numbers n such that the lunar product of the distinct lunar prime divisors of n is < n.

Original entry on oeis.org

100, 112, 113, 114, 115, 116, 117, 118, 119, 200, 211, 223, 224, 225, 226, 227, 228, 229, 300, 311, 322, 334, 335, 336, 337, 338, 339, 400, 411, 422, 433, 445, 446, 447, 448, 449, 500, 511, 522, 533, 544, 556, 557, 558, 559, 600, 611, 622

Offset: 1

David Applegate, Nov 11 2003

nonn

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Tanya Khovanova, Non Recursions
Index entries for sequences related to dismal (or lunar) arithmetic

A088478 Numbers n such that the lunar product of the distinct lunar prime divisors of n is <= n.

Original entry on oeis.org

9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 109, 112, 113, 114, 115, 116, 117, 118, 119, 129, 139, 149, 159, 169, 179, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 209, 211, 219, 223, 224, 225

Offset: 1

David Applegate, Nov 11 2003

nonn

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

A088479 Numbers n such that the lunar product of the distinct lunar prime divisors of n is equal to n.

Original entry on oeis.org

9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 109, 129, 139, 149, 159, 169, 179, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 209, 219, 239, 249, 259, 269, 279, 289, 290, 291, 292, 293, 294, 295, 296, 297

Offset: 1

David Applegate, Nov 11 2003

nonn

Includes the unit 9, the primes A087097, products of two distinct primes, etc. - N. J. A. Sloane, May 28 2011.

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087097.

A088481 Numbers n such that the lunar product of the distinct lunar prime divisors of n is > n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76

Offset: 1

David Applegate, Nov 11 2003

nonn

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

A134496 Numbers that are not lunar pseudoprimes.

Original entry on oeis.org

100, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156

Offset: 1

N. J. A. Sloane, Aug 15 2010

A number n is a lunar pseudoprime if it has no lunar divisors with length in the range 2, 3, ..., len(n)-1.
So the present sequence consists of the numbers which do have a lunar divisor of length in the range 2, 3, ..., len(n)-1.
Computed using David Applegate's programs.

			100 = 10*10.

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087062, etc.

cp's OEIS Frontend

A087036 Lunar cubes: n*n*n, where * is lunar multiplication.

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A087051 Lunar fourth powers: n*n*n*n, where * is lunar multiplication.

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A088473 Numbers n such that the lunar sum of the distinct lunar prime divisors of n is <= n.

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A088475 Numbers n such that the lunar sum of the distinct lunar prime divisors of n is >= n.

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A088476 Numbers n such that the lunar sum of the distinct lunar prime divisors of n is > n.

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A088477 Numbers n such that the lunar product of the distinct lunar prime divisors of n is < n.

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A088478 Numbers n such that the lunar product of the distinct lunar prime divisors of n is <= n.

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A088479 Numbers n such that the lunar product of the distinct lunar prime divisors of n is equal to n.

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A088481 Numbers n such that the lunar product of the distinct lunar prime divisors of n is > n.

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A134496 Numbers that are not lunar pseudoprimes.

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A087036 Lunar cubes: nnn, where * is lunar multiplication.

A087051 Lunar fourth powers: nnnn, where is lunar multiplication.