[seqfan] Re: A170817, A170818 xref suggested

Alois Heinz heinz at hs-heilbronn.de
Wed Dec 23 21:12:24 CET 2009

```Jonathan Post schrieb:
> A170818
> A170817
Both sequences have an erroneous a(39)=1, because 39=3*13 and 13=3*4+1.

A170817:

a:= n-> mul (i, i=map (x-> x[1], select (x-> isprime (x[1]) and
irem (x[1], 4)=1, ifactors(n)[2]))): seq (a(n), n=1..120);

1,1,1,1,5,1,1,1,1,5,1,1,13,1,5,1,17,1,1,5,1,1,1,1,5,
13,1,1,29,5,1,1,1,17,5,1,37,1,13,5,41,1,1,1,5,1,1,1,1,
5,17,13,53,1,5,1,1,29,1,5,61,1,1,1,65,1,1,17,1,5,1,1,
73,37,5,1,1,13,1,5,1,41,1,1,85,1,29,1,89,5,13,1,1,1,5,
1,97,1,1,5,101,17,1,13,5,53,1,1,109,5,37,1,113,1,5,29,13,
1,17,5

A170818:

a:= n-> mul (i, i=map (x-> x[1]^x[2], select (x-> isprime (x[1]) and
irem (x[1], 4)=1, ifactors(n)[2]))): seq (a(n), n=1..120);

1,1,1,1,5,1,1,1,1,5,1,1,13,1,5,1,17,1,1,5,1,1,1,1,25,
13,1,1,29,5,1,1,1,17,5,1,37,1,13,5,41,1,1,1,5,1,1,1,1,
25,17,13,53,1,5,1,1,29,1,5,61,1,1,1,65,1,1,17,1,5,1,1,
73,37,25,1,1,13,1,5,1,41,1,1,85,1,29,1,89,5,13,1,1,1,5,
1,97,1,1,25,101,17,1,13,5,53,1,1,109,5,37,1,113,1,5,29,
13,1,17,5

> [ ... ]
> The first composite values of A170817 are, of course, a(65) and a(85)?
This is true:

a(65)=65, a(85)=85, a(130)=65, a(145)=145, a(170)=85, a(185)=185,
a(195)=65, a(205)=205, a(221)=221, a(255)=85, a(260)=65, a(265)=265,
a(290)=145, a(305)=305, a(325)=65, a(340)=85, a(365)=365,
a(370)=185, a(377)=377, a(390)=65, a(410)=205, a(425)=85,
a(435)=145, a(442)=221, a(445)=445, a(455)=65, a(481)=481,
a(485)=485, a(493)=493 ...

Alois

```