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 1-3 of 3 results.

A083787 Sequence contains the prime signature pertaining to the n-th row of A083785.

Original entry on oeis.org

1, 2, 6, 60, 60, 60, 420
Offset: 1

Views

Author

Amarnath Murthy, May 07 2003

Keywords

Examples

			a(4) = 2^2*3*5 = 60 because A083785(4, 1) = 19940 = 2^2*5*997, (p^2*q*r) etc.

Crossrefs

Cf. A034173, A034174, A046523, A083785.

Formula

a(n) = A046523(A034173(n)). - Amiram Eldar, Jul 28 2024

Extensions

a(6)-a(7) from Jinyuan Wang, May 24 2020

A034173 a(n) is minimal such that prime factorizations of a(n), ..., a(n)+n-1 have same exponents.

Original entry on oeis.org

1, 2, 33, 19940, 204323, 380480345, 440738966073
Offset: 1

Views

Author

Dean Hickerson, Oct 01 1998

Keywords

Comments

a(8) > 10^13. - Donovan Johnson, Oct 20 2009
Don Reble has shown that a(8) < 1.9*10^42, cf. link.
From David Wasserman, Jan 05 2019: (Start)
a(8) <= 108111092880293127811946663766147737122,
a(9) <= 6850672946809600696044301071559918192380244,
a(10) <= 96037988156124494415303285590850571857698741869620,
a(11) <= 9044737840075556371215937303485030235666252755947862558252154847122. (End)

Examples

			a(4) = 19940 because 19940, ..., 19943 all have the form p^2 q r.

Links

Crossrefs

Cf. A034174.
Cf. A006558, A083790.
Cf. A052213, A052214, A175590, A218448. This sequence is the first column of A083785 and first row of A113456. The latter generalizes to arithmetic progressions with step d>=1. - M. F. Hasler, Oct 28 2012

Programs

  • PARI
    A034173(n)={my(f);for(k=1,oo,f=0;for(i=1,n, f==(f=vecsort(factor(k+n-i)[,2])) || i==1 || [k+=n-i; next(2)]);return(k))} \\ M. F. Hasler, Oct 23 2012

Formula

a(n) = A034174(n) - n + 1. - Max Alekseyev, Nov 10 2009
a(n) = A083785(n,1) = A113456(1,n); a(2) = A052213(1), a(3) = A052214(1), a(4) = A175590(1), a(5) = A218448(1), a(6) = A218448(62) = A218448(63)-1. - M. F. Hasler, Oct 28 2012

Extensions

a(7) from Donovan Johnson, Oct 20 2009
Don Reble link repaired by N. J. A. Sloane, Oct 24 2024

A034174 a(n) is minimal such that prime factorizations of a(n)-n+1, ..., a(n) have same exponents.

Original entry on oeis.org

1, 3, 35, 19943, 204327, 380480350, 440738966079
Offset: 1

Views

Author

Dean Hickerson, Oct 01 1998

Keywords

Comments

The final terms of the arithmetic progressions defined in A083785. - N. J. A. Sloane, Oct 18 2007
a(8) > 10^13. - Donovan Johnson, Oct 20 2009. [See Reble link for an upper limit.]
The main entry is A034173, which should be updated whenever something relevant is added here. - M. F. Hasler, Oct 28 2012

Examples

			a(4)=19943 because 19940, ..., 19943 all have the form p^2 q r.

Links

Crossrefs

Diagonal of A083785. Cf. A034173, A083785, A083787. See A034173 for more.

Programs

  • PARI
    A034174(n)={my(f); for(k=n, oo, f=0; for(i=0, n-1, f==(f=vecsort(factor(k-i)[, 2])) || !i || [k+=n-i-1; next(2)]); return(k))} \\ For illustrative purpose; not useful for n>=6. - M. F. Hasler, Oct 28 2012

Formula

a(n) = A034173(n) + n - 1. - Max Alekseyev, Nov 10 2009

Extensions

a(7) from Donovan Johnson, Oct 20 2009
Showing 1-3 of 3 results.

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