A063956 Sum of unitary prime divisors (A056169, A034444) of n.

0, 2, 3, 0, 5, 5, 7, 0, 0, 7, 11, 3, 13, 9, 8, 0, 17, 2, 19, 5, 10, 13, 23, 3, 0, 15, 0, 7, 29, 10, 31, 0, 14, 19, 12, 0, 37, 21, 16, 5, 41, 12, 43, 11, 5, 25, 47, 3, 0, 2, 20, 13, 53, 2, 16, 7, 22, 31, 59, 8, 61, 33, 7, 0, 18, 16, 67, 17, 26, 14, 71, 0, 73, 39, 3, 19, 18, 18, 79, 5, 0

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

a(n*m) = a(n) + a(m) - a(gcd(n^2, m)) - a(gcd(n, m^2)) for all n and m > 0 (conjecture). - Velin Yanev, Feb 17 2019

Example

Prime factors in 420 which have exponent=1 (i.e., unitary p-divisors) are {5,7}; sum = 12, so a(420)=12. (The sum of all its p-divisors, unitary and non-unitary, is A008472(420) = 17.)

Mathematica

Table[DivisorSum[n, # &, And[PrimeQ@ #, GCD[#, n/#] == 1] &], {n, 81}] (* Michael De Vlieger, Feb 17 2019 *)

Prog

(PARI) { for (n=1, 1000, f=factor(n)~; a=0; for (i=1, length(f), if (f[2, i]==1, a+=f[1, i])); write("b063956.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 04 2009

Crossrefs

Cf. A008472, A034444, A056169-A056172, A034387.

Sequence in context: A294141 A265513 A140508 * A351078 A128214 A307865

Adjacent sequences: A063953 A063954 A063955 * A063957 A063958 A063959

Keyword

nonn

Author

Labos Elemer, Sep 04 2001

Status

approved