|
%I #26 Oct 13 2021 10:31:57
%S 1,7,101,312,351,448,479,726,781,897,1040,1580,1605,2159,2339,2783,
%T 3298,3739,4485,4608,4650,4735,4776,4902,5473,6746,6894,6994,8353,
%U 8961,10117,10658,11714,12226,13758,14309,14729,15512,18446,18682
%N Numbers m such that A006218(m) is a perfect square.
%H Chai Wah Wu, <a href="/A175345/b175345.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..286 from Robert Israel)
%e If A027750 is displayed as a triangle where the row lengths are successive odd integers:
%e 1; <-- 1
%e 1, 2; 1,
%e 3; 1, 2, 4; 1,
%e 5; 1, 2, 3, 6; 1, 7: <-- 7
%e 1, 2, 4, 8; 1, 3, 9; 1, 2,
%e ...
%p N:= 10^5: # to get all entries up to N
%p A:= Vector(N, numtheory:-tau, datatype=integer[8]):
%p C:= Statistics:-CumulativeSum(A);
%p select(t -> issqr(round(C[t])), [$1..N]); # _Robert Israel_, May 19 2014
%o (PARI) lista(nn) = {s = 0; for (n=1, nn, s += numdiv(n); if (issquare(s), print1(n, ", ")););} \\ _Michel Marcus_, Oct 19 2015
%o (Python)
%o from sympy import integer_nthroot, divisor_count
%o A175345_list, k, c, = [], 1, 1
%o while k < 10**4:
%o if integer_nthroot(c,2)[1]: A175345_list.append(k)
%o k += 1
%o c += divisor_count(k) # _Chai Wah Wu_, Oct 11 2021
%Y Cf. A000005, A006218, A027750.
%K easy,nonn
%O 1,2
%A _Ctibor O. Zizka_, Apr 17 2010
|
