A351544 a(n) is the largest unitary divisor of sigma(n) such that its every prime factor also divides A003961(n), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.

1, 3, 1, 1, 1, 3, 1, 3, 1, 9, 1, 1, 1, 3, 1, 1, 1, 3, 1, 21, 1, 9, 1, 15, 1, 3, 5, 1, 1, 9, 1, 9, 1, 27, 1, 1, 1, 3, 1, 9, 1, 3, 1, 3, 1, 9, 1, 1, 1, 3, 1, 1, 1, 15, 1, 3, 5, 9, 1, 21, 1, 3, 1, 1, 7, 9, 1, 9, 1, 9, 1, 15, 1, 3, 1, 1, 1, 3, 1, 3, 1, 9, 1, 1, 1, 3, 5, 9, 1, 9, 1, 3, 1, 9, 1, 9, 1, 9, 13, 7, 1, 27

Offset

1,2

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = Product_{p^e || A000203(n)} p^(e*[p divides A003961(n)]), where [ ] is the Iverson bracket, returning 1 if p is a divisor of A003961(n), and 0 otherwise. Here p^e is the largest power of prime p dividing sigma(n).

a(n) = A000203(n) / A351546(n).

For all n >= 1, a(n) is a multiple of A351545(n).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351544(n) = { my(s=sigma(n), f=factor(s), u=A003961(n)); prod(k=1, #f~, if(!(u%f[k, 1]), f[k, 1]^f[k, 2], 1)); };

Crossrefs

Cf. A000203, A003961, A351545, A351546.

Cf. A342671, A349161, A349162.

Sequence in context: A325446 A337322 A090176 * A102396 A344852 A095960

Adjacent sequences: A351541 A351542 A351543 * A351545 A351546 A351547

Keyword

nonn

Author

Antti Karttunen, Feb 16 2022

Status

approved