A063070 - OEIS

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A063070

a(n) = phi(n) - d(n), where d(n) is the number of divisors function (A000005).

0, -1, 0, -1, 2, -2, 4, 0, 3, 0, 8, -2, 10, 2, 4, 3, 14, 0, 16, 2, 8, 6, 20, 0, 17, 8, 14, 6, 26, 0, 28, 10, 16, 12, 20, 3, 34, 14, 20, 8, 38, 4, 40, 14, 18, 18, 44, 6, 39, 14, 28, 18, 50, 10, 36, 16, 32, 24, 56, 4, 58, 26, 30, 25, 44, 12, 64, 26, 40, 16, 68, 12, 70, 32, 34, 30, 56, 16, 76, 22, 49, 36, 80, 12, 60, 38, 52, 32, 86, 12, 68, 38

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

It is known that a(n) >= 1 for n >= 31.

REFERENCES

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 11.

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

FORMULA

a(n) = A000010(n) - A000005(n). - Wesley Ivan Hurt, Nov 24 2021

MATHEMATICA

Table[EulerPhi[n] - DivisorSigma[0, n], {n, 100}] (* Wesley Ivan Hurt, Nov 24 2021 *)

PROG

(PARI) j=[]; for(n=1, 150, j=concat(j, eulerphi(n)-(numdiv(n)))); j

(PARI) { for (n=1, 1000, write("b063070.txt", n, " ", eulerphi(n) - numdiv(n)) ) } \\ Harry J. Smith, Aug 16 2009

CROSSREFS

Cf. A000010, A000005. A020488 gives n such that a(n) = 0.

Sequence in context: A246846 A292474 A127528 * A049802 A129240 A246816

Adjacent sequences: A063067 A063068 A063069 * A063071 A063072 A063073

KEYWORD

easy,sign

AUTHOR

Jason Earls, Aug 04 2001

STATUS

approved