A325962 a(1) = 1; for n > 1, a(n) is the largest k <= 1+A046666(n) such that n-k and n-(sigma(n)-k) are relatively prime, or -1 if no such nonnegative k exists.

1, 1, 0, 3, 0, 5, 0, 7, 7, 9, 0, 11, 0, 13, 10, 15, 0, 17, 0, 19, 18, 21, 0, 23, 21, 25, 24, 27, 0, 29, 0, 31, 28, 33, 30, 35, 0, 37, 36, 39, 0, 41, 0, 43, 40, 45, 0, 47, 43, 49, 44, 51, 0, 53, 50, 55, 54, 57, 0, 59, 0, 61, 60, 63, 60, 65, 0, 67, 64, 69, 0, 71, 0, 73, 72, 75, 70, 77, 0, 79, 79, 81, 0, 83, 80, 85, 82, 87, 0, 89, 82

Offset

1,4

Comments

a(n) is equal to A325817(n) only with odd primes and the even terms of A000396. a(n) = -1 only on odd perfect numbers, if such numbers exist. Otherwise a(n) = 2n - A325961(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n)

Formula

For all n, a(A065091(n)) = 0.

Prog

(PARI)
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A325962(n) = { my(s=sigma(n)); forstep(i=1+n-A020639(n), 0, -1, if(1==gcd(n-i, n-(s-i)), return(i))); (-1); };

Crossrefs

Cf. A000203, A000396, A020639, A046666, A065091, A324213, A325817, A325818, A325960, A325961, A325965, A325966.

Sequence in context: A160035 A281648 A353154 * A210451 A239233 A051704

Adjacent sequences: A325959 A325960 A325961 * A325963 A325964 A325965

Keyword

nonn

Author

Antti Karttunen, May 29 2019

Status

approved