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 A348740 Positions k where A348733(k) is not multiplicative. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers k with a factorization into coprime x and k/x with A348733(x) * A348733(k/x) <> A348733(k). LINKS Table of n, a(n) for n=1..46. 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 *) PROG (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)); CROSSREFS Cf. A003959, A034448, A348733, A348734, A348735. Cf. also A344702. Sequence in context: A251842 A105417 A105416 * A368191 A298222 A180465 Adjacent sequences: A348737 A348738 A348739 * A348741 A348742 A348743 KEYWORD nonn AUTHOR Antti Karttunen, Nov 05 2021 STATUS approved

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Last modified June 21 07:35 EDT 2024. Contains 373540 sequences. (Running on oeis4.)