A341612 Characteristic function of A341614: a(n) = 1 if sigma(n) <= 2n < A003961(n), 0 otherwise.

0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A252742(n) * A294935(n).

a(n) >= A341613(n).

Mathematica

f[1] = 1; f[n_] := Times @@ (NextPrime[#1]^#2 & @@@ FactorInteger[n]); a[n_] := Boole[DivisorSigma[1, n] <= 2*n < f[n]]; Array[a, 100] (* Amiram Eldar, Feb 22 2021 *)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A341612(n) = ((sigma(n)<=(2*n))&&((2*n)<A003961(n)));

Crossrefs

Cf. A000203, A003961, A252742, A294935, A341613, A341614.

Sequence in context: A360125 A324883 A106002 * A252742 A066247 A151774

Adjacent sequences: A341609 A341610 A341611 * A341613 A341614 A341615

Keyword

nonn

Author

Antti Karttunen, Feb 22 2021

Status

approved