A086664 a(n) = n - (sum of prime power components of n).

1, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 5, 0, 5, 7, 0, 0, 7, 0, 11, 11, 9, 0, 13, 0, 11, 0, 17, 0, 20, 0, 0, 19, 15, 23, 23, 0, 17, 23, 27, 0, 30, 0, 29, 31, 21, 0, 29, 0, 23, 31, 35, 0, 25, 39, 41, 35, 27, 0, 48

Offset

1,10

Comments

a(n) = 0 iff n is a prime power p^a, a >= 1.

Contribution from Daniel Forgues, Nov 16 2009: (Start)

a(n) = (product of prime power components of n) - (sum of prime power components of n).

a(1) = (product of prime power components of 1) - (sum of prime power components of 1)

a(1) = (empty product) - (empty sum) = 1 - 0 = 1. (End)

Links

Daniel Forgues, Table of n, a(n) for n = 1..100000

Formula

a(n) = n - A008475(n).

Example

a(1) = 1 - (0) = 1,
a(8) = 8 - (2^3) = 0,
a(10) = 10 - (2^1 + 5^1) = 3.

Mathematica

Join[{1}, Array[# - Total[MapApply[Power, FactorInteger[#]]] &, 100, 2]] (* Paolo Xausa, Mar 16 2024 *)

Prog

(PARI) sof(n)=local(x); x=factor(n); sum(i=1, length(x[, 1]), x[i, 1]^x[i, 2]); for(i=1, 60, print1(i-sof(i)", "))

Crossrefs

Cf. A008475.

Sequence in context: A369700 A347361 A175919 * A164736 A349343 A109753

Adjacent sequences: A086661 A086662 A086663 * A086665 A086666 A086667

Keyword

nonn

Author

Jon Perry, Jul 27 2003

Extensions

Corrected (a(1) changed from 0 to 1) and edited by Daniel Forgues, Nov 14 2009

Status

approved