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A055631 Sum of Euler's totient function phi of distinct primes dividing n. 6
0, 1, 2, 1, 4, 3, 6, 1, 2, 5, 10, 3, 12, 7, 6, 1, 16, 3, 18, 5, 8, 11, 22, 3, 4, 13, 2, 7, 28, 7, 30, 1, 12, 17, 10, 3, 36, 19, 14, 5, 40, 9, 42, 11, 6, 23, 46, 3, 6, 5, 18, 13, 52, 3, 14, 7, 20, 29, 58, 7, 60, 31, 8, 1, 16, 13, 66, 17, 24, 11, 70, 3, 72, 37, 6, 19, 16, 15, 78, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = Sum_{p divides n} p-1 = A008472(n) - A001221(n).

Additive with a(p^e) = p-1: a(10) = a(2*5) = a(2)+a(5) = (2-1)+(5-1) = 5; a(28) = a(2^2*7) = a(2^2)+a(7) = 1+6 = 7. - Vladeta Jovovic, Oct 23 2001

EXAMPLE

If n = p^w, a power of prime, then a(n) = p-1; if n = 2p, then a(n) = p = n/2.

MAPLE

with(numtheory); a := n -> add(f, f = map(phi, factorset(n)));

seq(a(n), n = 1..81);  # Peter Luschny, Mar 30 2014

MATHEMATICA

Join[{0}, Table[Total[EulerPhi[Transpose[FactorInteger[n]][[1]]]], {n, 2, 90}]] (* Harvey P. Dale, Oct 29 2012 *)

PROG

(PARI) A055631(n)=sum(i=1, #n=factor(n)~, n[1, i]-1) \\ M. F. Hasler, Nov 10 2016

CROSSREFS

Cf. A000010, A001221, A006093, A053570, A053571, A055632.

Sequence in context: A262663 A075348 A326062 * A234586 A186421 A004560

Adjacent sequences:  A055628 A055629 A055630 * A055632 A055633 A055634

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 06 2000

EXTENSIONS

Edited by M. F. Hasler, Nov 10 2016

STATUS

approved

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Last modified November 18 02:07 EST 2019. Contains 329242 sequences. (Running on oeis4.)