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A341612
Characteristic function of A341614: a(n) = 1 if sigma(n) <= 2n < A003961(n), 0 otherwise.
3
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 22 2021
STATUS
approved