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A318929
Intersection of A300216 and A306146.
0
1, 14, 22, 28, 44, 46, 56, 88, 92, 94, 112, 118, 166, 176, 184, 188, 214, 224, 236, 332, 334, 352, 358, 368, 376, 428, 448, 454, 472, 526, 664, 668, 694, 704, 716, 718, 736, 752, 766, 856, 896, 908, 934, 944, 958, 1006, 1052, 1126, 1174, 1328, 1336, 1388, 1408, 1432, 1436, 1438, 1472
OFFSET
1,2
COMMENTS
Except for a(1) every element is either twice a prime or twice a previous element.
Primes obtained when a term is divided by 2 are of the form 4k + 3, k > 0.
MAPLE
isA318929 := proc(n)
simplify(isA300216(n) and isA306146(n)) # reuses code of the other seqs.
end proc:
for n from 1 to 1500 do
if isA318929(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Feb 14 2019
MATHEMATICA
s[k_] := Sort[FactorInteger[k][[All, 2]]];
is300216[k_] := Switch[k, 2, False, 3, True, _, s[k] == s[EulerPhi[k]]];
d[k_] := If[k == 1, 1, Times @@ (1 - FactorInteger[k][[All, 1]])];
is306146[k_] := With[{dk = d[k]}, dk > 0 && d[EulerPhi[k]] == EulerPhi[dk]];
Select[Range[1500], is300216[#] && is306146[#]&] (* Jean-François Alcover, May 30 2024 *)
PROG
(PARI)
is300216(k) = vecsort(factor(k)[, 2]) == vecsort(factor(eulerphi(k))[, 2]);
a023900(n) = sumdivmult(n, d, d*moebius(d));
is306146(n) = sdm = a023900(n); if(sdm < 0, return(0), sdmphi = a023900(eulerphi(n)); eulerphi(sdm) == sdmphi);
isok(n) = is300216(n) && is306146(n); \\ Michel Marcus, Sep 13 2018
CROSSREFS
Sequence in context: A354811 A092112 A306146 * A187776 A048196 A305084
KEYWORD
nonn
AUTHOR
Torlach Rush, Sep 11 2018
EXTENSIONS
More terms from Michel Marcus, Sep 15 2018
STATUS
approved