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Nonsquarefree numbers n = p_1^s_1...p_m^s_m (m > 1) such that (p_i^s_i - 1) | n-1 for all 0 < i <= m.
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%I #24 Jul 28 2018 10:40:31

%S 12025,13833,35425,54145,89425,187461,203841,321201,499681,501025,

%T 566401,595441,717025,784225,856801,877825,965497,1080801,1165537,

%U 1299961,1335961,1439425,1566891,1658385,1935025,2058049,2514337,2668225,2817001,3078361

%N Nonsquarefree numbers n = p_1^s_1...p_m^s_m (m > 1) such that (p_i^s_i - 1) | n-1 for all 0 < i <= m.

%C If squarefree numbers were accepted, then Carmichael numbers would be included. - _Michel Marcus_, Mar 13 2018

%p isA292815 := proc(n)

%p local pf,pfs;

%p pfs := ifactors(n)[2] ;

%p if nops(pfs) = 1 or issqrfree(n) then

%p return false;

%p end if;

%p for pf in pfs do

%p if modp(n-1,op(1,pf)^op(2,pf)-1) > 0 then

%p return false;

%p end if;

%p end do:

%p true ;

%p end proc:

%p for n from 1 do

%p if isA292815(n) then

%p print(n) ;

%p end if;

%p end do: # _R. J. Mathar_, May 02 2018

%t fa[n_] := fa[n] = FactorInteger[n];

%t free[n_] := Union[Table[fa[n]〚i, 2〛, {i, Length[fa[n]]}]] == {1}

%t tes1[n_] := Union@Table[IntegerQ[(n - 1)/(fa[n][[i, 1]]^fa[n][[i, 2]] - 1)], {i, Length[fa[n]]}] == {True};

%t Select[1 + Range[3300200], ! free[#] && Length@fa[#] > 1 && tes1[#] &]

%o (PARI) isok(n) = {my(f = factor(n)); if ((#f~ > 1) && ! issquarefree(n), for (k=1, #f~, if ((n-1) % (f[k,1]^f[k,2] -1), return (0));); return (1);); return (0);} \\ _Michel Marcus_, Mar 05 2018

%Y Cf. A013929, A087442, A002997 (Carmichael numbers).

%K nonn

%O 1,1

%A _José María Grau Ribas_, Sep 24 2017