0,2

Definition of PrimeFactor_p or PF_p

PrimeFactor_p[n] = The largest power of p dividing n

It is written as PF_p[n]

PF_p,q,r[n] = PF_p[n]* PF_q[n]* PF_r[n]

PF_1[n] = 1

[How to compute c(m)]

Case of Base Primes = {2}{3}

a(0)=2^m, b(0)=2^m

a(n)=a(n-1)/PF_2[UnitarySigma[b(n-1)]]*PF_3[UnitarySigma[b(n-1)]]

b(n)=UnitarySigma[b(n-1)]/ PF_2,3[UnitarySigma[b(n-1)]]

IF b(k)=1 THEN END

c(m)=a(k)

Sequence gives c(m)

Factorization of term becomes 2^r*3^s.

Kohmoto computed up to c(12). Sugiyama computed up to c(20).

A034448 := proc(n) local ans, i: ans := 1: for i from 1 to nops(ifactors(n)[ 2 ]) do ans := ans*(1+ifactors(n)[ 2 ][ i ][ 1 ]^ifactors(n)[ 2 ] [ i ] [ 2 ]): od: ans ; end: PF := proc(n, p) local nshf, a ; a := 1; nshf := n ; while (nshf mod p ) = 0 do nshf := nshf/p ; a := a*p ; od: a ; end: A006519 := proc(n) PF(n, 2) ; end: A038500 := proc(n) PF(n, 3) ; end: A065330 := proc(n) local nshf ; nshf := n ; while (nshf mod 2 ) = 0 do nshf := nshf/2 ; od: while (nshf mod 3 ) = 0 do nshf := nshf/3 ; od: nshf ; end: A065331 := proc(n) n/A065330(n) ; end: A146892 := proc(n) local b, a, k ; b := [2^n] ; while op(-1, b) <> 1 do b := [op(b), A065330(A034448(op(-1, b))) ] ; od: a := 2^n ; for k from 2 to nops(b) do a := a/ A006519(A034448(op(k-1, b))) *A038500(A034448(op(k-1, b))) ; od: a ; end: seq(A146892(n), n=0..60) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 24 2009]

Cf. A146891.

Sequence in context: A074949 A078290 A065239 this_sequence A085804 A012125 A123190

Adjacent sequences: A146889 A146890 A146891 this_sequence A146893 A146894 A146895

nonn,uned

Yasutoshi Kohmoto zbi74583.boat at orange.zero.jp Yasutoshi, Apr 17 2009

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 24 2009