A120454 a(n) = ceiling(GPF(n)/LPF(n)) where GPF is greatest prime factor, LPF is least prime factor.

1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 2, 1, 1, 2, 1, 3, 3, 6, 1, 2, 1, 7, 1, 4, 1, 3, 1, 1, 4, 9, 2, 2, 1, 10, 5, 3, 1, 4, 1, 6, 2, 12, 1, 2, 1, 3, 6, 7, 1, 2, 3, 4, 7, 15, 1, 3, 1, 16, 3, 1, 3, 6, 1, 9, 8, 4, 1, 2, 1, 19, 2, 10, 2, 7, 1, 3, 1, 21, 1, 4, 4, 22, 10, 6, 1, 3, 2, 12, 11, 24, 4, 2, 1, 4, 4

Offset: 1

Author

Jonathan Vos Post, Aug 16 2006

Keywords

• easy
• nonn

Comments

Given GPF(n) and LPF(n), the sum is A074320, the difference is A046665 and the product is A066048. a(n) = 1 iff n is p^k iff n is in A000961.

Examples

			a(26) = ceiling(GPF(26)/LPF(26)) = ceiling(13/2) = 7.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000961, A006530, A020639, A024619, A046665, A066048, A069897, A074320.

Programs

Maple

A120454 := proc(n) local ifs ; if n = 1 then RETURN(1) ; else ifs := ifactors(n)[2] ; RETURN( ceil(op(1,op(-1,ifs))/op(1,op(1,ifs))) ) ; fi ; end ; for n from 1 to 100 do printf("%d, ",A120454(n)) ; od ; # R. J. Mathar, Dec 16 2006

Mathematica

a[n_] := Module[{p = FactorInteger[n][[;;, 1]]}, Ceiling[p[[-1]] / p[[1]]]]; Array[a, 100] (* Amiram Eldar, Oct 24 2024 *)

PARI

A120454(n) = if(1==n,1, my(f = factor(n), lpf = f[1, 1], gpf = f[#f~, 1]); ceil(gpf/lpf)); \\ Antti Karttunen, Sep 06 2018

Formula

a(n) = ceiling(A006530(n)/A020639(n)).

a(n) = A069897(n) + 1 if n is not a power of a prime (A024619), and 1 otherwise. - Amiram Eldar, Oct 24 2024

Extensions

Corrected and extended by R. J. Mathar, Dec 16 2006