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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 * A298222 A180465 A328886

Adjacent sequences:  A348737 A348738 A348739 * A348741 A348742 A348743

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 05 2021

STATUS

approved

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Last modified January 28 04:30 EST 2022. Contains 350654 sequences. (Running on oeis4.)