A348740 Positions k where A348733(k) is not multiplicative.

1444, 3249, 3364, 4332, 4563, 6498, 7220, 7569, 9126, 10092, 10108, 12996, 13924, 15138, 15884, 16245, 16820, 17689, 18252, 18772, 21125, 21660, 22743, 22815, 23104, 23548, 24548, 24964, 25992, 27436, 30276, 30324, 31329, 31684, 31941, 32490, 33212, 35378, 35739, 36100, 36504, 37004, 37845, 38988, 41209, 41772

Offset: 1

Author

Antti Karttunen, Nov 05 2021

Keywords

• nonn

Comments

Numbers k with a factorization into coprime x and k/x with A348733(x) * A348733(k/x) <> A348733(k).

Crossrefs

Cf. A003959, A034448, A348733, A348734, A348735.

Cf. also A344702.

Programs

Mathematica

f1[p_, e_] := (p + 1)^e; f2[p_, e_] := p^e + 1; a1[1] = 1; a1[n_] := GCD[Times @@ f1 @@@ (f = FactorInteger[n]), Times @@ f2 @@@ f]; f3[p_, e_] := a1[p^e]; a2[n_] := Times @@ f3 @@@ FactorInteger[n]; Position[Table[a2[n] - a1[n], {n, 1, 42000}], ?(# != 0 &)] // Flatten (* _Amiram Eldar, Nov 05 2021 *)

PARI

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A034448(n) = { my(f = factor(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); };
A348733(n) = gcd(A003959(n), A034448(n));
A348733mult(n) = { my(f = factor(n)); prod(k=1, #f~, A348733(f[k, 1]^f[k, 2])); };
isA348740(n) = (A348733(n)!=A348733mult(n));