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A323174 Deficiency computed for conjugated prime factorization: a(n) = A033879(A122111(n)). 14
1, 1, 1, 2, 1, 0, 1, 4, 5, -4, 1, 2, 1, -12, -3, 6, 1, 6, 1, -2, -19, -28, 1, 4, 14, -60, 19, -10, 1, -12, 1, 10, -51, -124, -12, 10, 1, -252, -115, 0, 1, -48, 1, -26, 7, -508, 1, 8, 41, 12, -243, -58, 1, 22, -64, -8, -499, -1020, 1, -12, 1, -2044, -17, 12, -168, -120, 1, -122, -1011, -54, 1, 18, 1, -4092, 26, -250, -39, -264, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Zeros occur at A122111(A000396(k)), k >= 1: 6, 40, 11264, 18253611008, ...
LINKS
FORMULA
a(n) = A033879(A122111(n)).
a(n) = 2*A122111(n) - A323173(n).
MATHEMATICA
A122111[n_] := Product[Prime[Sum[If[j<i, 0, 1], {j, #}]], {i, Max[#]}]&[ Flatten[Table[Table[PrimePi[f[[1]]], {f[[2]]}], {f, FactorInteger[n]}]]];
a[n_] := With[{k = A122111[n]}, 2k - DivisorSigma[1, k]];
Array[a, 80] (* Jean-François Alcover, Sep 23 2020 *)
PROG
(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
A323174(n) = { my(k=A122111(n)); ((2*k)-sigma(k)); }
CROSSREFS
Cf. also A323244.
Sequence in context: A262495 A352687 A336703 * A295683 A165519 A266972
KEYWORD
sign
AUTHOR
Antti Karttunen, Jan 10 2019
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)