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A225651 Numbers k that divide A000793(k).

%I A225651 #21 Aug 20 2021 04:23:08
%S A225651 1,2,3,4,6,10,12,14,15,20,21,24,30,35,36,39,40,42,44,52,55,56,60,65,
%T A225651 66,70,72,76,77,78,84,85,90,91,95,99,102,105,110,114,115,117,119,120,
%U A225651 126,130,132,133,136,138,140,143,152,153,154,155,156,161,165,170
%N A225651 Numbers k that divide A000793(k).
%C A225651 After 1, a subset of A225649.
%C A225651 Also, for all n, A225650(a(n)) = a(n) and A225655(a(n)) = A000793(a(n)).
%H A225651 Alois P. Heinz, <a href="/A225651/b225651.txt">Table of n, a(n) for n = 1..10000</a>
%p A225651 b:= proc(n, i) option remember; local p;
%p A225651       p:= `if`(i<1, 1, ithprime(i));
%p A225651       `if`(n=0 or i<1, 1, max(b(n, i-1),
%p A225651            seq(p^j*b(n-p^j, i-1), j=1..ilog[p](n))))
%p A225651     end:
%p A225651 g:=n->b(n, `if`(n<8, 3, numtheory[pi](ceil(1.328*isqrt(n*ilog(n)))))):
%p A225651 a:= proc(n) option remember; local k;
%p A225651       for k from 1+`if`(n=1, 0, a(n-1))
%p A225651       while not irem(g(k), k)=0 do od; k
%p A225651     end:
%p A225651 seq(a(n), n=1..70);  # _Alois P. Heinz_, May 22 2013
%t A225651 Reap[For[n=1, n <= 40, n++, If[Divisible[Max[LCM @@@ IntegerPartitions[n] ], n], Sow[n]]]][[2, 1]]
%t A225651 (* or, for a large number of terms: *)
%t A225651 b[n_, i_] := b[n, i] = Module[{p}, p = If[i<1, 1, Prime[i]]; If[n==0 || i<1, 1, Max[b[n, i-1], Table[p^j*b[n - p^j, i-1], {j, 1, Log[p, n] // Floor}]]]]; g[n_] := b[n, If[n<8, 3, PrimePi[Ceiling[1.328*Sqrt[n*Log[n] // Floor]]]]]; Reap[For[k=1, k <= 1000, k++, If[Divisible[g[k], k], Sow[ k]]]][[2, 1]] (* _Jean-François Alcover_, Feb 28 2016, after _Alois P. Heinz_ *)
%o A225651 (Scheme with _Antti Karttunen_'s IntSeq-library):
%o A225651 (define A225651 (MATCHING-POS 1 1 (lambda (i) (zero? (modulo (A000793 i) i)))))
%Y A225651 Cf. A225648, A225649, A225650, A225653, A225655-A225657.
%K A225651 nonn
%O A225651 1,2
%A A225651 _Antti Karttunen_, May 16 2013