login
A353766
a(n) = 1 if A353749(n) divides A353749(sigma(n)), and 0 otherwise. Here A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes.
2
1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
1
COMMENTS
For all multiperfect numbers, a(A007691(n)) = 1.
FORMULA
a(n) = 1 if A353762(n) = 1, otherwise 0.
MATHEMATICA
f[p_, e_] := (p - 1)*p^(e - 1)*If[p == 2, 1, NextPrime[p, -1]^e]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := Boole[Divisible[s[DivisorSigma[1, n]], s[n]] ]; Array[a, 120] (* Amiram Eldar, May 10 2022 *)
PROG
(PARI)
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A353749(n) = (eulerphi(n)*A064989(n));
A353766(n) = { my(s=sigma(n)); !(A353749(s)%A353749(n)); };
CROSSREFS
Characteristic function of A353764.
Cf. also A353633, A336546.
Sequence in context: A341629 A365429 A322860 * A178225 A373990 A264739
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 10 2022
STATUS
approved