[seqfan] Re: A possible list of new sequences

[Vladimir Shevelev]

Very thanks, Richard,
especially, for A063778 and  for an extension of A177029.
But I did not understand, why A086280?

Regards,
Vladimir

----- Original Message -----
From: Richard Mathar <mathar at strw.leidenuniv.nl>
Date: Saturday, May 1, 2010 16:27
Subject: [seqfan] Re: A possible list of new sequences
To: seqfan at seqfan.eu

> 
> Followup to http://list.seqfan.eu/pipermail/seqfan/2010-
> May/004550.html :
> 
> vs> I just have sent to OEIS the following two sequences :
> vs> 
> vs> %I A177025
> vs> %S A177025 
> 1,1,1,2,1,1,2,2,1,2,1,1,3,2,1,2,1,1,3,2,1,2,2,1,2,3,1,2,1,1,2,2,2,4,1,vs> %T A177025 1,2,2,1,2
> vs> %N A177025 Number of k>=3 for which n is k-gonal number 
> vs> %C A177025 Since n is always n-gonal number, then a(n)>=1. 
> Conjecture. Every positive integer appears in the sequence. 
> vs> %Y A177025 A000217 A000326 A000384 A000566 A000567 A176949 
> A176948 A176774 A176744 A176747 A176775 A175873 A176874 
> vs> %K A177025 nonn
> vs> %O A177025 3,4
> vs> %A A177025 Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 01 2010
> 
> A177025 starts as
> 1,1,1,2,1,1,2,2,1,2,1,1,3,2,1,2,1,1,3,2,1,2,2,1,2,3,1,2,1,1,2,2,2,4,1,1,2,2,1,
> 2,1,1,4,2,1,2,2,1,3,2,1,2,3,1,2,2,1,2,1,1,2,3,2,4,1,1,2,3,1,2,1,1,3,2,1,3,1,1,
> 4,2,1,2,2,1,2,2,1,2,3,2,2,2,2,3,1,1,2,3,1,2,1,1,4,2,1,2,1,1,3,3,1,2,2,1,3,2,1,4
> 
> The first occurrence of a=2,3,4,.. is at n = 6, 15, 36, 225 (see 
> A063778).
> See Also A139601, A139600 and A086280.
> 
> vs> %I A177029
> vs> %S A177029 6,9,10,12,16,18,22,24,25,27,30,33,34,35,39,40,42
> vs> %N A177029 Numbers m for which A177025(m)=2 
> vs> %C A177029 Numbers u for which A177025(u)=1 are listed by 
> A090467. 
> vs> %Y A177029 A177025 A090467 A177028 A000217 A000326 A000384 
> A000566 A000567 A176949 A176948 A176774 A176744 A176747 A176775 
> A175873 A176874 
> vs> %K A177029 nonn
> vs> %O A177029 1,1
> vs> %A A177029 Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 01 2010
> 
> On should mention that A177029 is a subsequence of A090466.
> A177029 starts
> 
> 6,9,10,12,16,18,22,24,25,27,30,33,34,35,39,40,42,46,48,49,52,54,57,58,60,63,65,
> 69,72,76,82,84,85,87,88,90,92,93,94,95,99,102,106,108,114,115,118,121,123,124,
> 125,129,130,132,133,138,142,147,150,155,159,160,162,166,168,169,172,174,177,
> 178,180,183,184,185,192,198,202,205,207,208,213,214,215,217,219,220,222,226,
> 228,234,237,240,243,244,245,247,249,250,252,253,258,259,260,262,264,265,267,
> 268,270,273,274,275,279,282,287,289,292,294,295,298,301,303,304,305,309,310,
> 312,318,327,328,334,335,339
> 
> Maple implementation of A177025:
> # see A139601 A139600 A086270
> kgonal := proc(n,k)
>         option remember ;
>         n/2*( (k-2)*n-k+4) ;
> end proc:
> 
> A177025 := proc(n)
>         local a,k,m ;
>         a := 0 ;
>         for k from 3 to n do
>                 for m from 0 do
>                         km := kgonal(m,k) ;
>                         if km = n then
>                                 a := a+1 ;
>                         elif m > n then
>                                 break;
>                         end if;
>                 end do:
>         end do:
>         a ;
> end proc:
> seq(A177025(n),n=3..120) ;
> 
> 
> 
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 Shevelev Vladimir‎