A353638 a(n) = 1 if n is odd and A064989(sigma(n)) < A064989(n), otherwise 0. Here A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

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) = A000035(n) * A348737(A064989(n)).

For n > 1, a(n) = A000035(n) - A353639(n). [Conjectured, see comments in A336702]

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); };
A353638(n) = ((n%2) && (A064989(sigma(n))<A064989(n)));

Crossrefs

Characteristic function of A348748 (see also A348738).

Cf. A000035, A000203, A064989, A336702, A348737, A353639.

Sequence in context: A257531 A151763 A353558 * A324908 A353760 A358770

Adjacent sequences: A353635 A353636 A353637 * A353639 A353640 A353641

Keyword

nonn

Author

Antti Karttunen, May 04 2022

Status

approved