cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A085273 Difference between n-th composite number and its largest prime divisor.

Original entry on oeis.org

2, 3, 6, 6, 5, 9, 7, 10, 14, 15, 15, 14, 11, 21, 20, 13, 24, 21, 25, 30, 22, 17, 28, 33, 19, 26, 35, 35, 33, 40, 23, 45, 42, 45, 34, 39, 51, 44, 49, 38, 29, 55, 31, 56, 62, 52, 55, 51, 46, 63, 69, 37, 70, 57, 66, 65, 75, 78, 41, 77, 68, 43, 58, 77, 85, 78, 69, 62, 47, 76, 93, 91
Offset: 1

Views

Author

Cino Hilliard, Aug 12 2003

Keywords

Examples

			For 91=7*13 we have 91-13 = 78.
For 92=2*2*23 we have 92-23 = 69.

Links

Crossrefs

Cf. A002808, A085271.

Programs

  • Mathematica
    DeleteCases[Table[n - FactorInteger[n][[-1, 1]], {n, 100}], 0 ] (* _Ivan Neretin, Jun 20 2019 *)
  • PARI
    cminusp2(n) = { for(x=2,n, forstep(p=x,2,-1, if(isprime(p) & x%p==0 & isprime(x)==0,print1(x-p,","); break); ) ) }

Extensions

Offset corrected by Ivan Neretin, Jun 20 2019

A091114 Number of partitions of n-th composite number containing the smallest prime factor: a(n) = A027293(A002808(n), A056608(n)).

Original entry on oeis.org

2, 5, 11, 11, 22, 42, 77, 77, 135, 231, 385, 385, 627, 1002, 627, 1575, 1575, 2436, 3718, 5604, 5604, 8349, 5604, 12310, 17977, 17977, 26015, 37338, 53174, 53174, 75175, 105558, 53174, 147273, 147273, 204226, 281589, 204226, 386155, 386155
Offset: 1

Views

Author

Reinhard Zumkeller, Feb 22 2004

Keywords

Comments

a(n) = A000041(A002808(n)) - A091094(n).
a(n) = A000041(A085271(n)). - Charlie Neder, Jan 10 2019

Examples

			n=2: A002808(2)=6=2*3 has A000041(6)=11 partitions: 6 = 5+1 = 4+2 = 4+1+1 = 3+3 = 3+2+1 = 3+1+1+1 = 2+2+2 = 2+2+1+1 = 2+1+1+1+1 = 1+1+1+1+1+1, 2 occurs in 5 partitions, therefore a(2)=5.

Crossrefs

Cf. A002808, A000041, A020639, A027293, A056608, A085271, A091109, A091094.

Programs

  • PARI
    lista(nn) = forcomposite(n=2, nn, print1(numbpart(n - divisors(n)[2]), ", ")); \\ Michel Marcus, Jan 11 2019

A091094 Number of partitions of n-th composite number not containing the smallest prime factor.

Original entry on oeis.org

3, 6, 11, 19, 20, 35, 58, 99, 96, 154, 242, 407, 375, 573, 1331, 861, 1435, 1282, 1886, 2745, 4539, 3961, 9279, 5667, 8038, 13208, 11323, 15836, 22001, 35960, 30383, 41715, 120351, 56953, 92670, 77363, 104566, 247050, 140668, 227999, 188397
Offset: 1

Views

Author

Reinhard Zumkeller, Feb 22 2004

Keywords

Comments

a(n) = A000041(A002808(n)) - A091114(n).
a(n) = A000041(A002808(n)) - A000041(A085271(n)). - Charlie Neder, Jan 11 2019

Crossrefs

Cf. A002808, A000041, A020639, A056608.

Extensions

Incorrect formula removed by Charlie Neder, Jan 11 2019

A085275 Sum of n-th composite number and its largest prime divisor.

Original entry on oeis.org

6, 9, 10, 12, 15, 15, 21, 20, 18, 21, 25, 28, 33, 27, 30, 39, 30, 35, 35, 34, 44, 51, 42, 39, 57, 52, 45, 49, 55, 50, 69, 51, 56, 55, 68, 65, 57, 66, 63, 76, 87, 65, 93, 70, 66, 78, 77, 85, 92, 77, 75, 111, 80, 95, 88, 91, 85, 84, 123, 91, 102, 129, 116, 99, 95, 104, 115, 124
Offset: 4

Views

Author

Cino Hilliard, Aug 12 2003

Keywords

Examples

			For 91=7*13 we have 91+13 = 104; for 92=2*2*23 we have 92+23 = 115.

Crossrefs

Cf. A085271, A085273.

Programs

  • PARI
    cminusp3(n) = { for(x=2,n, forstep(p=x,2,-1, if(isprime(p) & x%p==0 & isprime(x)==0, print1(x+p,","); break); ) ) }
Showing 1-4 of 4 results.

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