A353633 - OEIS

A353633

a(n) = 1 if A351546(n) is a unitary divisor of n, otherwise 0. Here A351546(n) is the largest unitary divisor of sigma(n) coprime with A003961(n).

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

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OFFSET

COMMENTS

For all known triperfect numbers, n = 1..6, a(A005820(n)) = 1.

For all known 5-multiperfect numbers, n = 1..65, a(A046060(n)) = 1.

For all known multiperfects m such that sigma(m) is also multiperfect, n = 1..23, a(A323653(n)) = 1.

Observation: Apparently, for no other odd terms than 1 of A006872, a(2*A006872(n)) = 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)) = [1 == A353668(n)] * [1 == gcd(A351546(n),A353667(n))], where [ ] are the Iverson brackets.

PROG

(PARI)

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

A351546(n) = { my(f=factor(sigma(n)), u=A003961(n)); prod(k=1, #f~, f[k, 1]^((0!=(u%f[k, 1]))*f[k, 2])); };

A353633(n) = { my(u=A351546(n)); (!(n%u) && 1==gcd(u, n/u)); };

CROSSREFS

Characteristic function of A351551.

Cf. A000203, A003961, A005820, A351546, A353667, A353668.

Cf. also A005820, A006872, A046060, A323653.

Sequence in context: A016335 A016373 A281815 * A205988 A167700 A010057

Adjacent sequences: A353630 A353631 A353632 * A353634 A353635 A353636

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 04 2022

STATUS

approved