A341613 Characteristic function for A341615: a(n) = 1 if sigma(n) < 2n < A003961(n), otherwise 0.

0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 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) * A294934(n).

a(n) <= A341612(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); };
A341613(n) = ((sigma(n)<(2*n))&&((2*n)<A003961(n)));

Crossrefs

Cf. A000203, A003961, A252742, A294934, A341613, A341614.

Sequence in context: A359467 A359469 A107078 * A163533 A354982 A020987

Adjacent sequences: A341610 A341611 A341612 * A341614 A341615 A341616

Keyword

nonn

Author

Antti Karttunen, Feb 22 2021

Status

approved