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A063956 Sum of unitary prime divisors (A056169, A034444) of n. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A128214 A307865 A219695

Adjacent sequences:  A063953 A063954 A063955 * A063957 A063958 A063959

KEYWORD

nonn

AUTHOR

Labos Elemer, Sep 04 2001

STATUS

approved

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Last modified July 13 04:31 EDT 2020. Contains 335673 sequences. (Running on oeis4.)