A336562 Number of pairs sigma(p^x), sigma(q^y) that are not coprime, where p^x and q^y are any two maximal prime power divisors of n, with p < q. a(1) = 0.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 3

Offset

1,30

Links

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

Index entries for sequences related to sigma(n)

Example

For n = 40 = 2^3 * 5^1, sigma(2^3) = 15 and sigma(5) = 6, so we have one such prime power pair that the gcd of their sum of divisors is larger than one (in this case gcd(15,6) = 3), thus a(40) = 1.
For n = 120 = 2^3 * 3^1 * 5^1, possible pairs are [sigma(8), sigma(3)], [sigma(8), sigma(5)] and [sigma(3), sigma(5)], with gcd(15,4) = 1, gcd(15,6) = 3 and gcd(4,6) = 2, thus there are two pairs that are not coprime, and a(120) = 2.

Prog

(PARI) A336562(n) = if(1==n, 0, my(f=factor(n), s=0); for(i=1, #f~, for(j=1+i, #f~, if(1!=gcd(sigma(f[i, 1]^f[i, 2]), sigma(f[j, 1]^f[j, 2])), s++))); (s));

Crossrefs

Cf. A000203, A051027, A324892, A336355, A336356, A336546, A336547 (positions of zeros), A336548 (of nonzero terms).

Sequence in context: A029429 A064559 A340998 * A067255 A065716 A079409

Adjacent sequences: A336559 A336560 A336561 * A336563 A336564 A336565

Keyword

nonn

Author

Antti Karttunen, Jul 27 2020

Status

approved