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

1,6

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.

Links

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

Formula

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

Example

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

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

Prog

(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

Crossrefs

Cf. A000040, A006530, A020639, A074320, A046665, A066048.

Sequence in context: A280274 A073408 A372572 * A321648 A330755 A316431

Adjacent sequences: A120451 A120452 A120453 * A120455 A120456 A120457

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 16 2006

Extensions

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

Status

approved